ICMS

Sep 7, 2009 - Sep 11, 2009

14 India Street, Edinburgh EH3 6EZ

Organisers

Name	Institution
Partington, Jonathan	University of Leeds
Pott, Sandra	University of Paderborn and University of Glasgow

 

This workshop will highlight some of the areas of operator theory where rapid developments have taken place in the last decade, and bring together mathematicians engaged in these different yet connected areas. Rather than concentrating on one narrow area, the workshop will explore three main strands:

• Applied Operator Theory
• Operator Theory and Complex Analysis
• Operator Theory and Harmonic Analysis

We will consider both the role of applications as a source of deep operator-theoretic questions and the role of Harmonic Analysis techniques in the theory of operators of function spaces, which is in turn relevant in applications. The aim of the workshop is to strengthen the interaction between researchers using operator theory, especially operators on analytic function spaces, for applications, and researchers working on harmonic analysis and operator theory on analytic function spaces from a more theoretical point of view.

Invited speakers

Aleman, Alexandru (Lund)
Badea, Catalin (Lille)
Ball, Joseph (Virginia Tech)
Baranov, Anton (St Petersburg State)
Batty, Charles (Oxford)
Bayart, Frederic (Clermont-Ferrand)
Bonami, Aline (Orleans)
Boulton, Lyonell (Heriot-Watt University)
Carbery, Tony (University of Edinburgh)
Curtain, Ruth (Groningen)
Dritschel, Michael (Newcastle)
Gillespie, Alastair (Edinburgh)
Gorkin, Pamela (Bucknell)
Grivaux, Sophie (Lille)
Haak, Bernhard (Universite de Bordeaux 1)
Haase, Markus (Delft)
Hytonen, Tuomas (Helsinki)
Jacob, Birgit (Paderborn)
Lacey, Michael (Georgia Tech)
Leblond, Juliette (INRIA)
Le Merdy, Christian (Besancon)
Lyubarskii, Yura (Trondheim)
McCarthy, John (Trinity College Dublin)
Power, Stephen (Lancaster)
Rochberg, Richard (St. Louis)
Sasane, Amol (London School of Economics and Political Science)
Shargorodsky, Eugene (King's College London)
Tretter, Christiane (Bern)
Wick, Brett (South Carolina)
Young, Nicholas (Leeds)

Numbers will be limited and participation is by invitation only.

This workshop is supported by:

EPSRC
SFC
LMS
Edinburgh Mathematical Society
Glasgow Mathematical Journal Trust

 

Arrangements

A map showing the places mentioned below and in the programme is available here.

Venue
The workshop will take place at the head-quarters of ICMS, 14 India Street, Edinburgh. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.

The ICMS travel pages contain advice on how to travel to Edinburgh. For local information the finding ICMS page shows the location of ICMS and contains useful maps of the city centre.

The seminar room at ICMS has 4 whiteboards, 2 overhead projectors, a data projector and laptop. If you are giving a talk we ask that you use our ICMS laptop and bring your talk on a memory stick or CD. If you wish your talk to be pre-loaded onto our laptop, you may email it in advance to Helene Frössling .

Wireless access is available throughout the ICMS building. There are also 4 public PCs which may be used at any time for internet access and to check email.

Accommodation
ICMS has booked accommodation for delegates in two locations: The Albany on Albany Street, and The Ballantrae Hotel on York Place. Delegates who asked to have accommodation reserved for them will be allocated a room in one of the two hotels. Participants are also free to make their own arrangements. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.

Meals and Refreshments
There will be an informal wine reception after the close of lectures on Monday 7 September.

Morning and afternoon refreshments will be provided on each day of the workshop.

Buffet lunches will be provided on Monday 7 and Friday 11 September at no cost to participants. For the remainder of the days, participants are free to go out for lunch and explore the many cafés, sandwich shops, restaurants and bars nearby. On arrival we will provide you with a ‘welcome’ pack which will contain information about eating places nearby.

The workshop dinner will take place on the evening of Thursday 10 September. The workshop grant will cover the cost of these meals.

Registration
Registration will take place on the morning of Monday 7 September.

Arrival
The main trainstation in Edinburgh is Waverley Station. From Waverley it is around 20-30 minutes walking distance to ICMS offices at India Street. There are currently major road works restricting where Princes Street can be crossed. Waverley Station is around 10 minutes away from the workshop hotels by foot. There is a taxi rank by track 11. Please note that many taxis only accept cash payment.

Edinburgh Airport is small and easy to find your way around. Airlink buses connect the airport to the city. Departures from outside the Domestic Arrivals lounge are frequent. Airlink buses terminate at Waverley Station on Waverley Bridge.

Coaches terminate at St Andrew's Bus Station. From here, you can easily reach York Place (which is the next street to the north of the bus station) and Albany Street.

On Sunday 6 September a major event is taking place in central Edinburgh in the evening. The Edinburgh International Festival Firework Concert is an annual event tempting thousands of people out from 7 pm and onwards. Please note that this is likely to affect travel times. The Airlink service will terminate in another location than Waverley Bridge. At the moment, it is unclear where, possibly St Andrew's Square which is five minutes from the hotels.

 

Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your bed and breakfast accommodation, tea/coffee throughout the workshop, lunch on Monday and Friday only, the wine reception, the informal supper on Tuesday, the buffet on Wednesday and the Workshop Dinner on Thursday evening.

If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with receipts and bank details. Please note that we cannot reimburse any item without a receipt.

Participation
Participation is by invitation only. The workshop will begin on Monday 7 September and finish on Friday 11 September 2009.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one. If you do require a visa, ICMS can provide a signed invitation letter.

Programme

Please note that this programme is subject to change

Sunday 6 September (this is an optional outing organised by Sandra Pott)

19.30

Meeting at Cafe Royal for a drink and then a short walk to Calton Hill (at 20.00) to watch the fireworks display (commencing 21.00). Please wear clothes and footwear suitable for a chilly night.

Monday 7 September

09.00 - 09.50	Registration and coffee/tea
09.50 - 10.00	Welcome!
10.00 - 11.00	Richard Rochberg (Washington University in St Louis) The Dirichlet space and related function spaces
11.00 - 11.30	Coffee break
11.30 - 12.00	Tony Carbery (University of Edinburgh) Almost-orthogonality in the Schatten-von Neumann classes
12.00 - 12.30	Sophie Grivaux (Universite Lille 1) A new class of frequently hypercyclic operators on Banach spaces
12.30 - 14.00	Lunch
14.00 - 15.00	Yura Lyubarskii (NTNU Trondheim) Riesz bases of reproducing kernels in Fock type spaces Abstract
15.00 - 15.30	Coffee break
15.30 - 16.00	Frederic Bayart (Clermont-Ferrand 2) Maximum modulus of random polynomials
16.00 - 16.30	Alexandru Aleman (University of Lund) A quantitative estimate for bounded point evaluations in $P^t(mu)$-spaces
16.30 - 18.00	Wine reception and poster session

 

Tuesday 8 September

09.00 - 10.00	Joseph Ball (Virginia Polytechnic Institute and State University) Function theory on the unit disk via the state-space method: extensions to multivariable functions and multidimensional linear systems
10.00 - 10.30	Coffee break
10.30 - 11.00	Michael Dritschel (University of Newcastle) Semigroup actions of reproducing kernel correspondences
11.00 - 11.30	Stephen Power (University of Lancaster) Operator theory and crystals
11.30 - 11.45	Break
11.45 - 12.15	Catalin Badea (Universite de Lille 1) Orbits with good or bad behaviour
12.15 - 14.00	Lunch
14.00 - 15.00	Pamela Gorkin (Bucknell University) Cyclic Blaschke products and composition operators
15.00 - 15.30	Coffee break
15.30 - 16.00	Christian Le Merdy (Universite de Franche-Comte) R-Bounded representations of amenable groups
16.00 - 16.30	Bernhard Haak (Universite de Bordeaux 1) Uniformly $gamma$-radonifyng families of operators Abstract
16.30 - 17.00	Markus Haase (University of Delft) Transference techniques and functional calculus
	Knowledge Transfer Event at the Royal Over-Seas League, 100 Princes Street
18.30 - 19.00	Arrival
19.00 - 20.00	Christiane Tretter (University of Bern) Operator theory and its applications Abstract
20.00 - 21.00	Wine reception and networking

 

Wednesday 9 September

09.00 - 10.00	John McCarthy (Washington University at St Louis and Trinity College Dublin) Distinguished varieties and algebraic pairs of isometries
10.00 - 10.30	Coffee break
10.30 - 11.00	Brett Wick (Georgia Institute of Technology) Corona theorems for multiplier algebras on B_n
11.00 - 11.30	Nicholas Young (University of Leeds) Boundary behaviour of functions in the Schur class of the bidisc
11.30 - 12.00	Break
12.00 - 12.30	Anton Baranov (St Petersburg State University) Feichtinger conjecture for reproducing kernels in model subspaces
	Lunch, then guided walking tour of Edinburgh's New Town

Thursday 10 September

09.00 - 10.00	Ruth Curtain (University of Groningen) Analyticity of Riccati equation solutions Abstract
10.00 - 10.30	Coffee break
10.30 - 11.00	Juliette Leblond (INRIA) Boundary value problems for the conjugate Beltrami equation in plane domains and constructive approximation in generalized Hardy spaces
11.00 - 11.30	Charles Batty (University of Oxford) Functional calculus and perturbations
11.30 - 12.00	Break
12.00 - 12.30	Amol Sasane (London School of Economics and Political Science) On the projective freeness of Banach algebras of measures
12.30 - 14.00	Lunch
14.00 - 15.00	Birgit Jacob (Universitaet Paderborn) Controllability of infinite-dimensional systems
15.00 - 15.30	Coffee break
15.30 - 16.00	Christiane Tretter (Universitaet Bern) Spectral inclusion for block operator matrices
16.00 - 16.30	Lyonell Boulton (Heriot-Watt University) Weyl-type theorems for limit sets of the finite section spectrum
16.30 - 17.00	Eugene Shargorodsky (King's College London) Some open problems in spectral theory

 

Friday 11 September

09.00 - 10.00	Aline Bonami (Universite d'Orleans) Bergman and Besov spaces of holomorphic functions in tube domains over symmetric cones Abstract
10.00 - 10.30	Coffee break
10.30 - 11.00	Tuomas Hytonen (University of Helsinki) Pseudo-localization of singular integrals in $L^p$
11.00 - 11.30	Alastair Gillespie (University of Edinburgh) Logarithms of invertible isometries
11.30 - 11.45	Break
11.45 - 12.45	Michael Lacey (Georgia Institute of Technology) Weighted inequalties for singular integrals
12.45 -13.30	Lunch buffet

Presentations:

Presentation Details
Aleman, Alexandru
A quantitative estimate for bounded point evaluations in $P^t(mu)$-spaces
View Abstract Hide Abstract
We will give a quantitative version of J. Thomson's theorem about bounded point evaluations in $P^t(mu)$. The approach is based on X. Tolsa's work on analytic capacity as well as Thomson's coloring scheme. This is joint work with S. Richter and C. Sundberg.
Badea, Catalin
Orbits with good or bad behaviour
View Abstract Hide Abstract
We discuss several properties of orbits of bounded linear operators acting on Hilbert or Banach spaces.
Ball, Joseph
Function theory on the unit disk via the state-space method: extensions to multivariable functions and multidimensional linear systems
View Abstract Hide Abstract
It is well known that the Schur-class functions on the unit disk (i.e., holomorphic functions on the unit disk with values in the space of contraction operators between two Hilbert spaces) can be characterized as the set of transfer functions associated with a discrete-time input/state/output dissipative linear system. The state-space method uses this representation in terms of a system matrix as a convenient coordinate system for the solution of a variety of function theory problems (e.g., zero-pole interpolation, Beurling-Lax-Halmos representation for a shift invariant subspace, Nevanlinna-Pick interpolation, Toeplitz-corona/Leech problem). We review these results and discuss recent extensions to more general settings, e.g., contractive multipliers on the Drury-Arveson space on the ball, the Schur-Agler class of functions on the polydisk, and noncommutative analogues of these spaces. These results in turn have interesting connections with robust control for linear systems with structured uncertainty.
Baranov, Anton
Feichtinger conjecture for reproducing kernels in model subspaces
View Abstract Hide Abstract
The Feichtinger conjecture states that any unit norm Bessel sequence in a separable Hilbert space is a finite union of Riesz basic sequences. This is a problem of high current interest, it was recently shown that it is equivalent to the famous Kadison--Singer conjecture in $C^*$-algebras as well as to some other important open problems of analysis. We consider a very special case of the Feichtinger conjecture where the space is a so-called model (or star-invariant) subspace $K_Theta = H^2 ominus Theta H^2$ of the Hardy space $H^2$ in the unit disc, associated with an inner function $Theta$, and the system in question is a system of normalized reproducing kernels $k^Theta_{lambda_n}$. In this case the Bessel property is equivalent to a Carleson type embedding theorem, whereas Riesz basic sequences of kernels correspond to interpolation sequences. In contrast to analogous problems in many other reproducing kernel Hilbert spaces, the Feichtinger conjecture for model subspaces is an open and, apparently, a difficult problem due to a rich and highly nontrivial structure of these spaces. Two results are discussed in the talk. First, we show that the Feichtinger conjecture is true for a Bessel system of reproducing kernels satisfying $sup_n |Theta(lambda_n)| < 1$ (points close to the spectrum of the inner function $Theta$). Second, we prove the Feichtinger conjecture in the case where $Theta$ is a one-component inner function, that is, the sublevel set ${|Theta|<varepsilon}$ is connected for some $varepsilon in (0,1)$.
Batty, Charles
Functional calculus and perturbations
View Abstract Hide Abstract
Functional calculus of sectorial operators is now well established, but it has also been considered for other classes of operators such as strip-type operators. Kalton has shown that bounded functional calculus is preserved by relatively bounded perturbations which are ``triangular''. We consider corresponding questions for strip-type and other operators.
Bayart, Frederic
Maximum modulus of random polynomials
View Abstract Hide Abstract
Recently, several problems occuring in modern functional or complex analysis have required, for their solution, to find polynomials with unimodular coefficients and with small sup-norm on the unit ball of a given Banach space. The first result in that direction is probably the Kahane-Salem-Zygmund inequality, where the supremum of a random polynomial on the unit polydisk is estimated. Several related inequalities where obtained by Boas, Defant, Garcia, Maestre and others. In this talk, we provide another estimation which is better than the previous ones. Our method uses the notion of metric entropy. Several applications will be given.
Bonami, Aline
Bergman and Besov spaces of holomorphic functions in tube domains over symmetric cones
View Abstract Hide Abstract
Abstract available as PDF file, linked from the programme above.
Boulton, Lyonell
Weyl-type theorems for limit sets of the finite section spectrum
View Abstract Hide Abstract
Let A be a self-adjoint densely defined operator acting on a Hilbert space. If B is A-compact, it is well-known that the essential spectra of A and A+B coincide. Let (L_n) be a nested sequence of finite dimensional subspaces contained in the domain of A and such that their union is dense in the graph norm. Denote by A_n the compression of A to (L_n). The spectrum of A is a subset of the limit of the spectra of A_n, but the latter set might differ from the former at a non-trivial "polluted" set. In this talk we argue that this polluted set has properties in common with the essential spectrum of A. We discuss the following question: what sort of conditions on B, in the spirit of relative compactness, guarantee that the polluted set of A equals the polluted set of A+B. The results announced are based on joint work with N. Boussaid and M. Lewin.
Carbery, Anthony
Almost-orthogonality in the Schatten-von Neumann classes
View Abstract Hide Abstract
We discuss what "almost-orthogonality" conditions on a sequence of operators in the Schatten-Von Neumann classes allow us to conclude that their sum is also in the class.
Curtain, Ruth
Analyticity of Riccati equation solutions
View Abstract Hide Abstract
Available as PDF linked from the programme
Dritschel, Michael
Semigroup actions of reproducing kernel correspondences
View Abstract Hide Abstract
Starting with a completely positive reproducing kernel over a set $X$ and a semigroup $S$ acting on $X$, we consider the linearization of the action of $S$ by means of operators on kernel correspondences. Various types of symmetry for the kernel make this possible. These symmetries can be expressed using cocycles and partial product systems, which themselves have a natural expression in terms of kernels. We also look at representations of correspondences and partial product systems. Finally, we consider how invariance of a kernel is reflected in the associated multiplier space.
Gillespie, Alastair
Logarithms of invertible isometries
View Abstract Hide Abstract
I shall discuss conditions under which an invertible isometry on a Banach space has a (bounded linear) logarithm, considering both the general situation and the case of certain specific translation operators.
Gorkin, Pamela
Cyclic Blaschke products and composition operators
View Abstract Hide Abstract
In this talk, we will show how to construct cyclic BLaschke products for composition operators induced by disc automorphisms. This construction provides a new characterization of Blaschke products that are not finite products of interpolating Blaschke products. Our characterization will show that a Blaschke product is not a finite product of interpolating Blaschke products with respect to a sequence of automorphisms tending to the boundary if and only if it ``almost'' has a universal Blaschke product as subfactor. (Joint work with Eva Gallardo)
Grivaux, Sophie
A new class of frequently hypercyclic operators on Banach spaces
View Abstract Hide Abstract
The study of the dynamics of a bounded linear operator T acting on a Banach space X is the study of the behaviour of the orbits {T^n x, n>0} of vectors x belonging to X. The operator T is said to be hypercyclic if it has a vector with dense orbit, and frequently hypercyclic if there exists a vector whose orbit visit any non empty open set at instants which form a set with positive lower density. In the work we present here, we generalize results obtained some years ago in collaboration with Frederic Bayart by showing that an operator on any separable complex Banach space which has "sufficiently many" eigenvectors associated to eigenvalues of modulus 1 is frequently hypercyclic.
Haak, Bernhard
Uniformly $gamma$-radonifyng families of operators
View Abstract Hide Abstract
Abstract available in PDF format linked form the programme above
Haase, Markus
Transference techniques and functional calculus
View Abstract Hide Abstract
We present latest results on transference techniques for (strongly continuous) groups and semigroups of linear operators and their effect on functional calculi for their generators and for sectorial operators with bounded imaginary powers. In the case of a discrete semigroup, i.e., a power-bounded operator, we extend a classical Hilbert space result of Peller's to arbitrary Banach spaces, making use of the notion of R-boundedness.
Hytönen, Tuomas
Pseudo-localization of singular integrals in $L^p$
View Abstract Hide Abstract
As an intermediate step in the development of a noncommutative Calderón-Zygmund theory, J. Parcet (JFA, 2009) established a new "pseudo-localization principle" of singular integral operators in $L^2$, which is also interesting on its own. I extend this result to the reflexive $L^p$ spaces, which was left open in Parcet's work. The new method of proof, based on martingale techniques, even slightly sharpens the original $L^2$ result.
Jacob, Birgit
Controllability of infinite-dimensional systems
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Intuitively the concept of controllability concerns the problem of steering a system into a given state in a certain time. An infinite-dimensional system is called exact controllable in time t if for every pair of initial and final states, one can find an input function such that the state of the system matches both the initial condition at time 0 and the final condition at time t. It has been noted in the literature that exact controllability rarely holds if the input space is one dimensional, and therefore we study weaker notions such as null controllability and approximate controllability as well. In this talk we mainly focus on theoretical operator methods and moment methods to address controllability problems. In 1992, Russell and Weiss generalized the Hautus-Popov lemma to systems described by bounded operators and they conjectured that the generalized Hautus-Popov lemma characterizes exact controllability for all infinite-dimensional systems. For a wide class of infinite-dimensional systems the controllability problem can be translated into a weighted interpolation problem by vector valued analytic functions. This enables us to characterize controllability in terms of Carleson measures and Carleson embeddings.
Lacey, Michael
Weighted Inequalties for Singular Integrals
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I will survey recent weighted results for singular integrals. In particular, characterizations of two-weight inequalities for maximal truncations of singular integrals, joint work with Uriate-Tuero and Sawyer. And a new proof of the linear bound the linear A_2 bound for Haar shift operators, joint with Reguera-Rodriguez and Petermichl. This new proof does not use Bellman techniques.
Le Merdy, Christian
R-Bounded representations of amenable groups
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Let G be a amenable group, let X be a Banach space and let T be a bounded representation of G on X. Under some mild assumptions, we show that if the range of T is R-bounded, then T extends to a bounded homomorphism from the group C*-algebra of G into B(X). Moreover this homomorphism is necessarily R-bounded. This extends to the Banach space setting a theorem of Day and Dixmier saying that any bounded representation of an amenable group on Hilbert space is unitarizable. We obtain additional results and complements when G is either Z, R or T and/or when X has property (alpha).
Leblond, Juliette
Boundary value problems for the conjugate Beltrami equation in plane domains and constructive approximation in generalized Hardy spaces
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In order to solve boundary value problems for the conductivity equation, or equivalently for the conjugate Beltrami equation, in plane domains, we introduce generalized Hardy spaces of solutions. Whenever the conductivity coefficient is smooth enough, they share a number of fundamental properties with the classical Hardy classes, and Dirichlet problems are well-posed. As a consequence, some bounded extremal problems can be stated and solved in these spaces, that allow to get constructive solutions to Cauchy type issues for the above equations. With a particular conductivity coefficient, and in the annular framework, this serves as a model for an application to plasma shaping (thermonuclear fusion, plasma confinment in tokamaks), for which computations are done with Bessel-exponential like basis functions.
Lyubarskii, Yura
Riesz bases of reproducing kernels in Fock type spaces
View Abstract Hide Abstract
Abstract available as a PDF document linked from the programme above.
McCarthy, John
Distinguished varieties and algebraic pairs of isometries
View Abstract Hide Abstract
A distinguished variety is an algebraic set in ${mathbb C}^2$ that is contained in $ {mathbb D}^2 cup {mathbb T}^2 cup {mathbb E}^2$, where ${mathbb D}$ is the unit disk, ${mathbb T}$ is the unit circle, and ${mathbb E}$ the exterior of the closed disk. An algebraic pair of isometries is a pair of commuting pure isometries that is annihilated by some polynomial. First, I will describe how distinguished varieties arose in operator theory in the first place. Then, I will explain why any algebraic pair of isometries must have a minimal polynomial whose zero set is a distinguished variety. Finally, I will talk about the fact that cyclic algebraic pairs of isometries are characterized by their minimal polynomial, up to being "nearly unitarily equivalent", which means each one is unitarily equivalent to the other restricted to a finite codimensional invariant subspace. This is joint work with Jim Agler and Greg Knese.
Power, Stephen
Operator theory and crystals
View Abstract Hide Abstract
I will outline some joint work in progress (with John Owen) on new functional analysis perspectives for infinite bar-joint constraint frameworks and models in crystallography. Of particular interest are the well-constrained frameworks that "satisfy Maxwell counting".
Rochberg, Richard
The Dirichlet Space and Related Function Spaces.
View Abstract Hide Abstract
Recent progress in understanding the classical Dirichlet space has also expanded the analogy between the Dirichlet space and the Hardy space. I will recall results about the Hardy space and then discuss recent progress in understanding the Dirichlet space and related spaces. I will then discuss extensions of the ideas and a number of open questions.
Sasane, Amol
On the projective freeness of Banach algebras of measures
View Abstract Hide Abstract
We will address the question of whether every square idempotent matrix P with entries in certain convolution Banach algebras of measures supported in [0,+infty) is conjugate (by an invertible matrix) to a matrix of the form diag(I_k, 0). The Banach algebras of measures we consider arise naturally in control theory as classes of stable impulse responses, and the relevance in control theory of the problem (of determining whether or not these Banach algebras are projective free or not) will also be explained.
Tretter, Christiane
Spectral inclusion for block operator matrices
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Block operator matrices arise frequently in mathematical physics, e.g. when considering systems of (partial) differential equations. In this talk we consider block operator matrices with bounded and unbounded entries. The main result is a refined spectral enclosure by means of the quadratic numerical range.
Wick, Brett
Corona Theorems for Multiplier Algebras on B_n
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Carleson's Corona Theorem from the 1960's has served as a major motivation for many results in complex function theory, operator theory and harmonic analysis. In its simplest form, the result states that for two bounded analytic functions, f_1 and f_2, on the unit disc with no common zeros, it is possible to find two other bounded analytic functions, g_1 and g_2, such that f_1g_1+f_2g_2=1. Moreover, the functions g_1 and g_2 can be chosen with some norm control. In this talk we will discuss an exciting new generalization of this result to certain function spaces on the unit ball in several complex variables.
Young, Nicholas
Boundary behaviour of functions in the Schur class of the bidisc
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Bounded analytic functions on the bidisc have much more interesting boundary behaviour than those on the one-dimensional disc. Even if rational they can have singularities at points on the torus (that is, points to which they cannot be continuously extended). I will describe how Hilbert space methods yield results on the nature of these singularities, and in particular lead to a two-dimensional Caratheodory theorem on continuity of gradients. This is joint work with Jim Agler (UCSD) and John E. McCarthy (Washington University).

Participants

Name	Institution
Aleman, Alexandru	University of Lund
Badea, Catalin	Universite de Lille
Ball, Joseph	Virginia Polytechnic Institute and State University
Baranov, Anton	St. Petersburg State University
Batty, Charles	University of Oxford
Bayart, Frederic	Clermont-Ferrand 2
Bonami, Aline	Universite d'Orleans
Boulton, Lyonell	Heriot-Watt University
Carbery, Anthony	University of Edinburgh
Curtain, Ruth	University of Groningen
Dritschel, Michael	University of Newcastle
Elliott, Samuel	University of Leeds
Gillespie, Alastair	University of Edinburgh
Gorkin, Pamela	Bucknell University
Grivaux, Sophie	Universite Lille 1
Haak, Bernhard	Université Bordeaux 1
Haase, Markus	University of Delft
Hytönen, Tuomas	University of Helsinki
Jacob, Birgit	Universitaet Paderborn
Kerr, Robert	University of Glasgow
Lacey, Michael	Georgia Institute of Technology
Le Merdy, Christian	Universite de Franche-Comte
Leblond, Juliette	INRIA
Lyubarskii, Yura	NTNU Trondheim
McCarthy, John	Trinity College Dublin
Miheisi, Nazar	University of Leeds
Partington, Jonathan	University of Leeds
Pickering, James	University of Newcastle
Pott, Sandra	University of Paderborn and University of Glasgow
Power, Stephen	University of Lancaster
Pozzi, Elodie	Universite Claude-Bernard Lyon
Rochberg, Richard	Washington University in St Louis
Sasane, Amol	London School of Economics and Political Science
Sehba, Benoit Florent	University of Glasgow
Shargorodsky, Eugene	King's College London
Tretter, Christiane	Universitaet Bern
Wick, Brett	Georgia Institute of Technology
Wynn, Andrew	University of Oxford
Young, Nicholas	University of Leeds