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.
Author(s): Daniel Girela Alvarez, Cristobal Gonzalez Enriquez
Publisher: Universidad de Málaga. UMA
Year: 2007
Language: English
Pages: C, xvi, 162, B
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
