Topics in Complex Analysis and Operator Theory
About this Title
Óscar Blasco, Universidad de Valencia, Valencia, Spain, José A. Bonet, Universidad Politénica de Valencia, Valencia, Spain, José M. Calabuig, Universidad Politécnica de Valencia, Valencia, Spain and David Jornet, Universidad Politécnica de Valencia, Valencia, Spain, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 561
ISBNs: 978-0-8218-5275-0 (print); 978-0-8218-8495-9 (online)
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 Paweł Domański; 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 Rodríguez-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. Rodríguez, and E.A. Sánchez-Pérez; On the spectra of algebras of analytic functions, by D. Carando, D. García, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Díaz-Madrigal, M.J. Martín, and D. Vukotić; 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. Peláez.
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.
Graduate students and research mathematicians interested in complex analysis and operator theory.
Table of Contents
- Paweł Domański – Notes on Real Analytic Functions and Classical Operators
- John E. McCarthy – Shining a Hilbertian lamp on the bidisk
- V. V. Peller – Selected problems in perturbation theory
- Luis Rodríguez-Piazza – Composition operators on Hardy-Orlicz spaces
- Oscar Blasco – Remarks on weighted mixed norm spaces
- J. M. Calabuig, J. Rodríguez and E. A. Sánchez-Pérez – Interpolation subspaces of of a vector measure and norm inequalities for the integration operator
- Daniel Carando, Domingo García, Manuel Maestre and Pablo Sevilla-Peris – On the spectra of algebras of analytic functions
- Manuel D. Contreras, Santiago Díaz-Madrigal, María J. Martín and Dragan Vukotić – Holomorphic self-maps of the disk intertwining two linear fractional maps
- Konstantin M. Dyakonov – -type estimates via Garsia-type norms
- Jordi Pau and José Ángel Peláez – Volterra type operators on Bergman spaces with exponential weights