Derivatives of Inner Functions
Derivatives of Inner Functions

Author: Javad Mashreghi

Publisher: Springer Science & Business Media

Published: 2012-11-14

Total Pages: 176

ISBN-13: 1461456118

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​Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since early last century, and the literature on this topic is vast. Therefore, this book is devoted to a concise study of derivatives of these objects, and confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. The goal is to provide rapid access to the frontiers of research in this field. This monograph will allow researchers to get acquainted with essentials on inner functions, and it is self-contained, which makes it accessible to graduate students.

The Theory of H ( b ) Spaces
The Theory of H ( b ) Spaces

Author: Emmanuel Fricain

Publisher: Cambridge University Press

Published: 2016-10-20

Total Pages: 641

ISBN-13: 1107027780

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In two volumes, this comprehensive treatment covers all that is needed to understand and appreciate this beautiful branch of mathematics.

The Theory of H(b) Spaces: Volume 2
The Theory of H(b) Spaces: Volume 2

Author: Emmanuel Fricain

Publisher: Cambridge University Press

Published: 2016-10-20

Total Pages: 641

ISBN-13: 1316351920

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An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

Introduction to Model Spaces and their Operators
Introduction to Model Spaces and their Operators

Author: Stephan Ramon Garcia

Publisher: Cambridge University Press

Published: 2016-05-17

Total Pages: 339

ISBN-13: 1316390438

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The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

Invariant Subspaces of the Shift Operator
Invariant Subspaces of the Shift Operator

Author: Javad Mashreghi

Publisher: American Mathematical Soc.

Published: 2015-04-23

Total Pages: 330

ISBN-13: 1470410451

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This volume contains the proceedings of the CRM Workshop on Invariant Subspaces of the Shift Operator, held August 26-30, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The main theme of this volume is the invariant subspaces of the shift operator (or its adjoint) on certain function spaces, in particular, the Hardy space, Dirichlet space, and de Branges-Rovnyak spaces. These spaces, and the action of the shift operator on them, have turned out to be a precious tool in various questions in analysis such as function theory (Bieberbach conjecture, rigid functions, Schwarz-Pick inequalities), operator theory (invariant subspace problem, composition operator), and systems and control theory. Of particular interest is the Dirichlet space, which is one of the classical Hilbert spaces of holomorphic functions on the unit disk. From many points of view, the Dirichlet space is an interesting and challenging example of a function space. Though much is known about it, several important open problems remain, most notably the characterization of its zero sets and of its shift-invariant subspaces. This book is co-published with the Centre de Recherches Mathématiques.