Topics in Complex Analysis and Operator Theory

✍ Scribed by Daniel Girela Alvarez, Cristobal Gonzalez Enriquez

• Publisher: Universidad de Málaga. UMA
• Year: 2007
• Tongue: English
• Leaves: 180
• Category: Library

✦ Synopsis

This volume comprises the conference proceedings of the \Winter School
in Complex Analysis and Operator Theory", held in Antequera, Malaga,
Spain, February 5-9, 2006. This winter school was organized as part of the
activities of the Spanish network \Complex Variables, Function Spaces and
Operators between them". This network is currently composed by approximately
70 researchers of 14 Spanish universities whose main areas of research
are Complex Analysis and Operator Theory and is supported by grants from
the Spanish \Ministerio de Educacion y Ciencia" (acciones complementarias
MTM2004-21420-E and MTM2006-26627-E).
Complex Analysis and Operator Theory are two of the most classical
branches of mathematical analysis and they are very closely related. Furthermore,
they have close links with others such as Harmonic Analysis,
Probability, Functional Analysis and Geometry. The interplay between all
these branches of mathematics gives rise to very beautiful results and makes
our area of research so nice and alive.

✦ Table of Contents

Cover

S Title

TOPICS IN COMPLEX ANALYSIS AND OPERATOR THEORY

Copyright (C) 2007 by Los autores
ISBN: 978-84-9747-174-9

Contents

Preface

List of Participants

Program

Part I Articles

 CLASS OF INTEGRAL OPERATORS ON SPACES OF ANALYTIC FUNCTIONS
      1. Introduction
      2. Some spaces of analytic functions
      3. Motivation and Examples
      4. Boundedness and Compactness I. Hardy spaces
      5. Boundedness and Compactness II. Bergman spaces
      6. The bilinear map (f; g) ----> Tgf
      7. Similarity to a contraction. A short digression
      8. A few remarks about spectrum and invariant subspaces
      References

 ASYMPTOTIC FORMULAS AND ZERO-DISTRIBUTION OF CERTAIN ENTIRE FUNCTIONS
      1. Introduction
      2. Functions with zeros on a regular strip
      3. Valiron's class
      4. Comments on the last Lemma
      5. The Balasov class
      6. Two solutions
      References

 DYNAMICS OF LINEAR OPERATORS
      1. Hypercyclicity
           1.1. Introduction: Hypercyclic and chaotic operators.
           1.2. The Hypercyclicity Criterion
      2. Frequent hypercyclicity
           2.1. Frequently hypercyclic operators.
           2.2. The set of frequently hypercyclic vectors.
      3. Ergodicity
           3.1. Ergodic theoretic methods in linear dynamics.
           3.2. Invariant Gaussian measures for linear operators.
           3.3. The unimodular eigenvalue criterion.
      References

 AN ELEMENTARY INTRODUCTION TO CLARK MEASURES
      Preface
      1. De nition of Clark measures
      2. Basic properties of Clark measures
      3. Angular derivatives
      4. The Aleksandrov operator
      5. Composition operators
      6. Sarason's theorem: (weak) compactness of C' on L1
      7. Shapiro's theorem: when C' in K(H2)?
      8. Di erences of composition operators
      9. Value distribution results
      10. Model spaces, spectral measures and the theorem of Poltoratski
      References

Part II Research Problems

 SOME OPEN PROBLEMS ON A CLASS OF INTEGRAL OPERATORS ON SPACES OF ANALYTIC FUNCTIONS
      References

 SOME PROBLEMS ON CARLESON MEASURES FOR BESOV-SOBOLEV SPACES