Hilbert Spaces of Analytic Functions ( CRM Proceedings & Lecture Notes )

Publication series :CRM Proceedings & Lecture Notes

Author: Javad Mashreghi;Thomas Ransford;Kristian Seip  

Publisher: American Mathematical Society‎

Publication year: 2010

E-ISBN: 9781470415853

P-ISBN(Paperback): 9780821848791

Subject: O1 Mathematics

Keyword: 暂无分类

Language: ENG

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Hilbert Spaces of Analytic Functions

Description

Hilbert spaces of analytic functions are currently a very active field of complex analysis. The Hardy space is the most senior member of this family. However, other classes of analytic functions such as the classical Bergman space, the Dirichlet space, the de Branges-Rovnyak spaces, and various spaces of entire functions, have been extensively studied. These spaces have been exploited in different fields of mathematics and also in physics and engineering. For example, de Branges used them to solve the Bieberbach conjecture. Modern control theory is another place that heavily exploits the techniques of analytic function theory. This book grew out of a workshop held in December 2008 at the CRM in Montréal and provides an account of the latest developments in the field of analytic function theory.

Chapter

Title page

Contents

List of participants

List of speakers

Preface

Canonical de Branges–Rovnyak model transfer-function realization for multivariable Schur-class functions

Two variations on the Drury–Averson space

The norm of a truncated Toeplitz operator

Approximation in weighted Hardy spaces for the unit disc

Some remarks on the Toeplitz corona problem

Regularity on the boundary in spaces of holomorphic functions on the unit disk

The search for singularities of solutions to the Dirichlet problem: Recent developments

Invariant subspaces of the Dirichlet space

Arguments of zero sets in the Dirichlet space

Questions on Volterra operators

Nonhomogeneous div-curl decompositions for local Hardy spaces on a domain

On the Bohr radius for simply connected plane domains

Completeness of the system {𝑓(𝜆_{𝑛}𝑧)} in 𝐿ₐ²[Ω]

A formula for the logarithmic derivative and its applications

Composition operators on the minimal Möbius invariant space

Whether regularity is local for the generalized Dirichlet problem

Back Cover

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