Lectures On Analytic Function Spaces And Their Applications

Author : Javad Mashreghi
Publisher : Springer Nature
Page : 426 pages
File Size : 48,7 Mb
Release : 2023-11-14
Category : Mathematics
ISBN : 9783031335723

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Lectures on Analytic Function Spaces and their Applications by Javad Mashreghi Pdf

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.

Author : Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Publisher : Springer Nature
Page : 487 pages
File Size : 54,5 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9783031392702

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Function Spaces, Theory and Applications by Ilia Binder,Damir Kinzebulatov,Javad Mashreghi Pdf

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 also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.

Author : Alexandru Aleman,Haakan Hedenmalm,Dmitry Khavinson,Mihai Putinar
Publisher : Springer
Page : 281 pages
File Size : 46,9 Mb
Release : 2019-05-30
Category : Mathematics
ISBN : 9783030146405

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Analysis of Operators on Function Spaces by Alexandru Aleman,Haakan Hedenmalm,Dmitry Khavinson,Mihai Putinar Pdf

This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.

Author : Evgeny Abakumov,Anton Baranov,Alexander Borichev,Konstantin Fedorovskiy,Joaquim Ortega-Cerdà
Publisher : Springer Nature
Page : 223 pages
File Size : 43,7 Mb
Release : 2021-11-19
Category : Mathematics
ISBN : 9783030744175

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Extended Abstracts Fall 2019 by Evgeny Abakumov,Anton Baranov,Alexander Borichev,Konstantin Fedorovskiy,Joaquim Ortega-Cerdà Pdf

This book collects the abstracts of the mini-courses and lectures given during the Intensive Research Program “Spaces of Analytic Functions: Approximation, Interpolation, Sampling” which was held at the Centre de Recerca Matemàtica (Barcelona) in October–December, 2019. The topics covered in this volume are approximation, interpolation and sampling problems in spaces of analytic functions, their applications to spectral theory, Gabor analysis and random analytic functions. In many places in the book, we see how a problem related to one of the topics is tackled with techniques and ideas coming from another. The book will be of interest for specialists in Complex Analysis, Function and Operator theory, Approximation theory, and their applications, but also for young people starting their research in these areas.

Author : Carl C. Cowen, Jr.,Barbara I. MacCluer
Publisher : CRC Press
Page : 404 pages
File Size : 54,5 Mb
Release : 1995-04-27
Category : Mathematics
ISBN : 0849384923

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Composition Operators on Spaces of Analytic Functions by Carl C. Cowen, Jr.,Barbara I. MacCluer Pdf

The study of composition operators lies at the interface of analytic function theory and operator theory. Composition Operators on Spaces of Analytic Functions synthesizes the achievements of the past 25 years and brings into focus the broad outlines of the developing theory. It provides a comprehensive introduction to the linear operators of composition with a fixed function acting on a space of analytic functions. This new book both highlights the unifying ideas behind the major theorems and contrasts the differences between results for related spaces. Nine chapters introduce the main analytic techniques needed, Carleson measure and other integral estimates, linear fractional models, and kernel function techniques, and demonstrate their application to problems of boundedness, compactness, spectra, normality, and so on, of composition operators. Intended as a graduate-level textbook, the prerequisites are minimal. Numerous exercises illustrate and extend the theory. For students and non-students alike, the exercises are an integral part of the book. By including the theory for both one and several variables, historical notes, and a comprehensive bibliography, the book leaves the reader well grounded for future research on composition operators and related areas in operator or function theory.

Author : Javad Mashreghi
Publisher : American Mathematical Soc.
Page : 0 pages
File Size : 51,9 Mb
Release : 2010
Category : Mathematics
ISBN : 0821848798

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Hilbert Spaces of Analytic Functions by Javad Mashreghi Pdf

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. This provides an account of the latest developments in the field of analytic function theory.

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 50,7 Mb
Release : 2003
Category : Function spaces
ISBN : 9780821832691

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Function Spaces by Krzysztof Jarosz Pdf

This volume presents papers from the Fourth Conference on Function Spaces. The conference brought together mathematicians interested in various problems within the general area of function spaces, allowing for discussion and exchange of ideas on those problems and related questions. The lectures covered a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $Lp$-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and related subjects. Included are 26 articles written by leading experts. Known results, open problems, and new discoveries are featured. Most papers are written for nonexperts, so the book can serve as a good introduction to the material presented.

Author : Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík
Publisher : Walter de Gruyter
Page : 495 pages
File Size : 46,9 Mb
Release : 2012-12-19
Category : Mathematics
ISBN : 9783110250428

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Function Spaces, 1 by Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík Pdf

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Author : S. Saitoh,N. Hayashi,M. Yamamoto
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 43,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475732986

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Analytic Extension Formulas and their Applications by S. Saitoh,N. Hayashi,M. Yamamoto Pdf

Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few. Audience: Researchers and graduate students in complex analysis, partial differential equations, analytic number theory, operator theory and inverse problems.

Author : M. F. Atiyah,J. Eells,K. M. Hoffman,L. Hörmander,C. E. Rickart,H. Rossi,S. Smale,F. Treves,J. Wermer
Publisher : Springer
Page : 170 pages
File Size : 45,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540361459

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Lectures in Modern Analysis and Applications I by M. F. Atiyah,J. Eells,K. M. Hoffman,L. Hörmander,C. E. Rickart,H. Rossi,S. Smale,F. Treves,J. Wermer Pdf

This lecture series was presented by a consortium of universities in conjunction with the U.S. Air Force Office of Scientific Research during the period 1967-1969 in Washington, D.C. and at the University of Maryland. The series of lectures was devoted to active basic areas of contemporary analysis which is important in or shows potential in real-world applications. Each lecture presents a survey and critical review of aspects of the specific area addressed, with emphasis on new results, open problems, and applications. This volume contains nine lectures in the series; subsequent lectures will also be published.

Author : Michael Cwikel,Laura De Carli,Mario Milman
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 52,6 Mb
Release : 2007
Category : Interpolation
ISBN : 9780821842072

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Interpolation Theory and Applications by Michael Cwikel,Laura De Carli,Mario Milman Pdf

This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 442 pages
File Size : 52,5 Mb
Release : 2011-08-22
Category : Mathematics
ISBN : 9781400840557

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Functional Analysis by Elias M. Stein,Rami Shakarchi Pdf

This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject. A comprehensive and authoritative text that treats some of the main topics of modern analysis A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables Key results in each area discussed in relation to other areas of mathematics Highlights the organic unity of large areas of analysis traditionally split into subfields Interesting exercises and problems illustrate ideas Clear proofs provided

Author : Dorothee Haroske,Thomas Runst,Hans-Jürgen Schmeisser
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 46,5 Mb
Release : 2003-02-24
Category : Mathematics
ISBN : 3764369353

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Function Spaces, Differential Operators and Nonlinear Analysis by Dorothee Haroske,Thomas Runst,Hans-Jürgen Schmeisser Pdf

This volume is dedicated to our teacher and friend Hans Triebel. The core of the book is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA--01) held in Teistungen, Thuringia / Germany, from June 28 to July 4,2001, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: • Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.

Author : D. Butkovic,H. Kraljevic,S. Kurepa
Publisher : Springer
Page : 254 pages
File Size : 40,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540393566

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Functional Analysis by D. Butkovic,H. Kraljevic,S. Kurepa Pdf

Author : Aleksander Pełczyński
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 42,7 Mb
Release : 1977-12-31
Category : Mathematics
ISBN : 9780821816806

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Banach Spaces of Analytic Functions and Absolutely Summing Operators by Aleksander Pełczyński Pdf

This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.