Topics in complex analysis and operator theory : Third Winter School Complex Analysis and Operator theory, February 2-5, 2010, Universidad Politécnica de Valencia, Valencia, Spain / Oscar Blasco [and three others], editors.

Format:

Book

Conference/Event

Author/Creator:

Winter School on Complex Analysis and Operator Theory, Corporate Author.

Contributor:

Blasco, Oscar, 1959- editor.

Universidad Politécnica de Valencia, issuing body.

Conference Name:

Winter School on Complex Analysis and Operator Theory (3rd : 2010 : Universidad Politécnica de Valencia), issuing body.

Winter School on Complex Analysis and Operator Theory.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 561

Contemporary mathematics, 561 0271-4132

Language:

English

Subjects (All):

Geometric function theory--Congresses.

Geometric function theory.

Analytic functions--Congresses.

Analytic functions.

Linear operators--Congresses.

Linear operators.

Physical Description:

1 online resource (266 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society ; [Madrid] : Real Sociedad Matematica Espanola, [2012]

Language Note:

English

Summary:

This book contains the lecture notes as well as some invited papers presented at the Third Winter School in Complex Analysis, Operator Theory and Applications held February 2-5, 2010, in Valencia, Spain. The book is divided into two parts. The first is an extended self-contained version of the mini-courses taught at the School. The papers in this first part are: Notes on real analytic functions and classical operators, by Pawel Domanski; Shining a Hilbertian lamp on the bidisk, by John E. McCarthy; Selected problems in perturbation theory, by Vladimir V. Peller; and Composition operators on Hardy-Orlicz spaces, by Luis Rodriguez-Piazza. The second part consists of several research papers on recent advances in the area and some survey articles of an expository character. The articles in this second part are: Remarks on weighted mixed norm spaces, by O. Blasco; Interpolation subspaces of $L^1$ of a vector measure and norm inequalities for the integration operator, by J.M. Calabuig, J. Rodriguez, and E.A. Sanchez-Perez; On the spectra of algebras of analytic functions, by D. Carando, D. Garcia, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Diaz-Madrigal, M.J. Martin, and D. Vukotic; ABC-type estimates via Garsia-type norms, by K.M. Dyakonov; and Volterra type operators on Bergman spaces with exponential weights, by J. Pau and J.A. Pelaez. The topics selected for the mini-courses cover several aspects of complex analysis and operator theory that play important roles in understanding connections between different areas that are considered in fashion these days. This part is aimed at graduate students and young researchers. The courses are self-contained, focusing on those aspects that are basic and that can lead the readers to a quick understanding of the theories presented in each topic. They start with the classical results and reach a selection of open problems in each case. The research and survey articles are aimed at young researchers in the area, as well as post-doc and senior researchers interested in complex analysis and operator theory. This book is published in cooperation with Real Sociedad Matematica Espanola.

Contents:

Preface

List of Participants

Mini-courses

Notes on Real Analytic Functions and Classical Operators

1. Lecture 1: Operator relevant properties of the space of real analytic functions

2. Lecture 2: Composition operators on the space of real analytic functions

3. Lecture 3: Differential and convolution operators on the space of real analytic functions

4. Lecture 4: Isomorphism of the spaces of real analytic functions

References

Shining a Hilbertian lamp on the bidisk

1. Lecture 1: Model Theory

8. Lifshits-Krein trace formulae

9. Koplienko-Neidhardt trace formulae

10. Perturbations of class _{ }

11. Perturbations of normal operators

Composition operators on Hardy-Orlicz spaces

Introduction

1. Composition operators on Hardy spaces

2. Hardy-Orlicz spaces

3. Carleson measures and compactness of composition operators

4. Carleson measures and Nevanlinna counting function

Articles

Remarks on weighted mixed norm spaces

1. Introduction and preliminaries

2. Generalities on weights.

4. Some applications.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-8495-6