Javad Mashreghi's Books

A Primer on the Dirichlet Space

By: Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford

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A Primer on the Dirichlet Space

By: Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford

The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.

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Page Count

227

Publisher

Cambridge University Press

Published Date

ISBN 10

1107729777

ISBN 13

9781107729773

Introduction to Model Spaces and their Operators

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

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Introduction to Model Spaces and their Operators

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.

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Page Count

339

Publisher

Cambridge University Press

Published Date

ISBN 10

1107108748

ISBN 13

9781107108745

The Theory of H(b) Spaces: Volume 2

By: Emmanuel Fricain,Javad Mashreghi

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The Theory of H(b) Spaces: Volume 2

By: Emmanuel Fricain,Javad Mashreghi

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.

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Page Count

641

Publisher

Cambridge University Press

Published Date

ISBN 10

1316351920

ISBN 13

9781316351925

Derivatives of Inner Functions

By: Javad Mashreghi

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Derivatives of Inner Functions

By: Javad Mashreghi

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.

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Page Count

176

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461456118

ISBN 13

9781461456117

The Theory of H ( b ) Spaces

By: Emmanuel Fricain,Javad Mashreghi

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The Theory of H ( b ) Spaces

By: Emmanuel Fricain,Javad Mashreghi

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

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641

Publisher

Cambridge University Press

Published Date

ISBN 10

1107027780

ISBN 13

9781107027787

Function Theory and ℓp Spaces

By: Raymond Cheng,Javad Mashreghi,William T. Ross

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Function Theory and ℓp Spaces

By: Raymond Cheng,Javad Mashreghi,William T. Ross

The classical ℓp sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces ℓpA of analytic functions whose Taylor coefficients belong to ℓp. Relations between the Banach space ℓp and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of ℓpA and a discussion of the Wiener algebra ℓ1A. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.

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Page Count

219

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470455935

ISBN 13

9781470455934

The Theory of H(b) Spaces

Volume 2

By: Emmanuel Fricain,Javad Mashreghi

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The Theory of H(b) Spaces

Volume 2

By: Emmanuel Fricain,Javad Mashreghi

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Page Count

640

Published Date

ISBN 10

1139226762

ISBN 13

9781139226769

Finite Blaschke Products and Their Connections

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

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Finite Blaschke Products and Their Connections

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered. Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.

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Page Count

340

Publisher

Springer

Published Date

ISBN 10

3319782479

ISBN 13

9783319782478

Derivatives of Inner Functions

By: Javad Mashreghi

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Derivatives of Inner Functions

By: Javad Mashreghi

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176

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Springer Science & Business Media

Published Date

ISBN 10

1461456118

ISBN 13

9781461456117

Representation Theorems in Hardy Spaces

By: Javad Mashreghi

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Representation Theorems in Hardy Spaces

By: Javad Mashreghi

This self-contained text provides an introduction to a wide range of representation theorems and provides a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane.

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Page Count

385

Publisher

Cambridge University Press

Published Date

ISBN 10

0521517680

ISBN 13

9780521517683

Operator Theory by Example

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

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Operator Theory by Example

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.

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Page Count

529

Publisher

Oxford University Press

Published Date

ISBN 10

019267885X

ISBN 13

9780192678850

Hilbert Spaces of Analytic Functions

By: Javad Mashreghi,Thomas Ransford,Kristian Seip

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Hilbert Spaces of Analytic Functions

By: Javad Mashreghi,Thomas Ransford,Kristian Seip

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 Montreal and provides an account of the latest developments in the field of analytic function theory. Titles in this series are co-published with the Centre de Recherches Mathematiques. (CRMP/51)

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Page Count

214

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821870459

ISBN 13

9780821870457

A Primer on the Dirichlet Space

By: Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford

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A Primer on the Dirichlet Space

By: Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford

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Solve jigsaw puzzle

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Page Count

226

Publisher

Cambridge University Press

Published Date

ISBN 10

1107047528

ISBN 13

9781107047525

Book's by Javad Mashreghi

A Primer on the Dirichlet Space

A Primer on the Dirichlet Space

Introduction to Model Spaces and their Operators

Introduction to Model Spaces and their Operators

The Theory of H(b) Spaces: Volume 2

The Theory of H(b) Spaces: Volume 2

Derivatives of Inner Functions

Derivatives of Inner Functions

The Theory of H ( b ) Spaces

The Theory of H ( b ) Spaces

Function Theory and ℓp Spaces

Function Theory and ℓp Spaces

The Theory of H(b) Spaces

The Theory of H(b) Spaces

Finite Blaschke Products and Their Connections

Finite Blaschke Products and Their Connections

Derivatives of Inner Functions

Derivatives of Inner Functions

Representation Theorems in Hardy Spaces

Representation Theorems in Hardy Spaces

Operator Theory by Example

Operator Theory by Example

Hilbert Spaces of Analytic Functions

Hilbert Spaces of Analytic Functions

A Primer on the Dirichlet Space

A Primer on the Dirichlet Space

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