Blaschke Products And Their Applications
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Blaschke Products And Their Applications
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Author : Javad Mashreghi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-05
Blaschke Products And Their Applications written by Javad Mashreghi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-05 with Mathematics categories.
Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields such as approximation theory, differential equations, dynamical systems, harmonic analysis, to name a few. Additionally, this volume illustrates the historical roots of Blaschke products and highlights key research on this topic. For nearly a century, Blaschke products have been researched. Their boundary behaviour, the asymptomatic growth of various integral means and their derivatives, their applications within several branches of mathematics, and their membership in different function spaces and their dynamics, are a few examples of where Blaschke products have shown to be important. The contributions written by experts from various fields of mathematical research will engage graduate students and researches alike, bringing the reader to the forefront of research in the topic. The readers will also discover the various open problems, enabling them to better pursue their own research.
Blaschke Products And Their Applications
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Author : Javad Mashreghi
language : en
Publisher: Springer
Release Date : 2012-10-05
Blaschke Products And Their Applications written by Javad Mashreghi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-05 with Mathematics categories.
Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields such as approximation theory, differential equations, dynamical systems, harmonic analysis, to name a few. Additionally, this volume illustrates the historical roots of Blaschke products and highlights key research on this topic. For nearly a century, Blaschke products have been researched. Their boundary behaviour, the asymptomatic growth of various integral means and their derivatives, their applications within several branches of mathematics, and their membership in different function spaces and their dynamics, are a few examples of where Blaschke products have shown to be important. The contributions written by experts from various fields of mathematical research will engage graduate students and researches alike, bringing the reader to the forefront of research in the topic. The readers will also discover the various open problems, enabling them to better pursue their own research.
Hankel Operators And Their Applications
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Author : Vladimir Peller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hankel Operators And Their Applications written by Vladimir Peller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func tions. Hankel operators can be defined as operators having infinite Hankel matrices (i. e. , matrices with entries depending only on the sum of the co ordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Han kel matrices was obtained by Kronecker, who characterized Hankel matri ces of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1, which defines Hankel operators and presents their basic properties. We consider different realiza tions of Hankel operators and important connections of Hankel operators with the spaces BMa and V MO, Sz. -Nagy-Foais functional model, re producing kernels of the Hardy class H2, moment problems, and Carleson imbedding operators.
An Introduction To Infinite Products
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Author : Charles H. C. Little
language : en
Publisher: Springer Nature
Release Date : 2022-01-10
An Introduction To Infinite Products written by Charles H. C. Little and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-10 with Mathematics categories.
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.
Operators And Hardy Classes
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-09
Operators And Hardy Classes written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-09 with Mathematics categories.
Operators and Hardy Classes is a comprehensive and engaging introduction to the fundamental concepts and applications of linear operators and Hardy classes in mathematical analysis. This book provides a thorough understanding of these essential mathematical tools, exploring their properties, spectral theory, and diverse applications across various branches of mathematics. Delve into the world of operators, including shift, Toeplitz, Hankel, composition, multiplication, and weighted composition operators, and uncover their crucial role in complex analysis, harmonic analysis, approximation theory, control theory, and mathematical physics. Discover the rich theory and fascinating connections between operators and Hardy classes, revealing their profound implications in function theory, interpolation theory, and probability theory. With numerous illustrative examples and applications, this book brings abstract concepts to life. Explore the interplay between operators and Hardy classes in action, witnessing their practical relevance in a wide range of disciplines. Whether you are a student seeking a comprehensive introduction to these topics or a seasoned researcher looking to expand your knowledge, this book is an invaluable resource. Key Features: * Provides a comprehensive overview of linear operators and Hardy classes, their properties, and spectral theory. * Explores the interplay between operators and Hardy classes, uncovering their significance in various mathematical fields. * Includes numerous illustrative examples and applications, demonstrating the practical relevance of the theoretical developments. * Serves as an essential reference for students, researchers, and professionals in mathematical analysis and related fields. With its clear explanations, insightful discussions, and extensive coverage of topics, Operators and Hardy Classes is the definitive guide to these fundamental mathematical concepts and their applications. Embark on a journey through the captivating world of operators and Hardy classes, and gain a deeper understanding of their profound significance in modern mathematics. If you like this book, write a review!
Representation Theorems In Hardy Spaces
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Author : Javad Mashreghi
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-19
Representation Theorems In Hardy Spaces written by Javad Mashreghi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-19 with Mathematics categories.
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.
Derivatives Of Inner Functions
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Author : Javad Mashreghi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-14
Derivatives Of Inner Functions written by Javad Mashreghi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-14 with Mathematics categories.
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.
Introduction To Model Spaces And Their Operators
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Author : Stephan Ramon Garcia
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-17
Introduction To Model Spaces And Their Operators written by Stephan Ramon Garcia and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-17 with Mathematics categories.
A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.
Lectures On Analytic Function Spaces And Their Applications
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Author : Javad Mashreghi
language : en
Publisher: Springer Nature
Release Date : 2023-10-13
Lectures On Analytic Function Spaces And Their Applications written by Javad Mashreghi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-13 with Mathematics categories.
The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.
Reproducing Kernels And Their Applications
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Author : S. Saitoh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Reproducing Kernels And Their Applications written by S. Saitoh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997. As specified in the invitation of the President Professor Robert P. Gilbert of the ISAAC, we organized the session on Reproducing Kerneis and Their Applications. In our session, we presented 24 engaging talks on topics of current interest to the research community. As suggested and organized by Professor Gilbert, we hereby publish its Proceedings. Rather than restricting the papers to Congress participants, we asked the Ieading mathematicians in the field of the theory of reproducing kern eIs to submit papers. However, due to time restrietions and a compulsion to limit the Proceedings a reasonable size, we were unable to obtain a comprehensive treatment of the theory of reproducing kernels. Nevertheless, we hope this Proceedings of the First International Conference on reproducing kerneis will become a significant reference volume. Indeed, we believe that the theory of reproducing kernels will stand out as a fundamental and beautiful contribution in mathematical sciences with a broad array of applications to other areas of mathematics and science. We would like to thank Professor Robert Gilbert for his substantial contri bu tions to the Congress and to our Proceedings. We also express our sincere thanks to the staff of the University of Delaware for their manifold cooperation in organizing the Congress.