The Dirichlet Space And Related Function Spaces

The Dirichlet Space And Related Function Spaces Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of The Dirichlet Space And Related Function Spaces book. This book definitely worth reading, it is an incredibly well-written.

The Dirichlet Space and Related Function Spaces

Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick
The Dirichlet Space and Related Function Spaces Book PDF

Author : Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick
Publisher : American Mathematical Soc.
Page : 536 pages
File Size : 42,6 Mb
Release : 2019-09-03
Category : Dirichlet principle
ISBN : 9781470450823

Get Book

The Dirichlet Space and Related Function Spaces by Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick Pdf

The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.

Lectures on Analytic Function Spaces and their Applications

Javad Mashreghi
Lectures on Analytic Function Spaces and their Applications Book PDF

Author : Javad Mashreghi
Publisher : Springer Nature
Page : 426 pages
File Size : 41,9 Mb
Release : 2023-11-14
Category : Mathematics
ISBN : 9783031335723

Get Book

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.

A Primer on the Dirichlet Space

Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford
A Primer on the Dirichlet Space Book PDF

Author : Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford
Publisher : Cambridge University Press
Page : 227 pages
File Size : 52,8 Mb
Release : 2014-01-16
Category : Mathematics
ISBN : 9781107729773

Get Book

A Primer on the Dirichlet Space by Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford Pdf

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.

Recent Advances in Operator-Related Function Theory

Alec L. Matheson,Conference on Recent Advances in Operator Related Function Theory,Conference on Recent Advances in Operato
Recent Advances in Operator Related Function Theory Book PDF

Author : Alec L. Matheson,Conference on Recent Advances in Operator Related Function Theory,Conference on Recent Advances in Operato
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 48,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839256

Get Book

Recent Advances in Operator-Related Function Theory by Alec L. Matheson,Conference on Recent Advances in Operator Related Function Theory,Conference on Recent Advances in Operato Pdf

The articles in this book are based on talks at a conference devoted to interrelations between function theory and the theory of operators. The main theme of the book is the role of Alexandrov-Clark measures. Two of the articles provide the introduction to the theory of Alexandrov-Clark measures and to its applications in the spectral theory of linear operators. The remaining articles deal with recent results in specific directions related to the theme of the book.

Function Spaces, Theory and Applications

Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Function Spaces Theory and Applications Book PDF

Author : Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Publisher : Springer Nature
Page : 487 pages
File Size : 42,8 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9783031392702

Get Book

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.

Maximal Function Methods for Sobolev Spaces

Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Maximal Function Methods for Sobolev Spaces Book PDF

Author : Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 45,7 Mb
Release : 2021-08-02
Category : Education
ISBN : 9781470465759

Get Book

Maximal Function Methods for Sobolev Spaces by Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas Pdf

This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

Pick Interpolation and Hilbert Function Spaces

Jim Agler,John E. McCarthy
Pick Interpolation and Hilbert Function Spaces Book PDF

Author : Jim Agler,John E. McCarthy
Publisher : American Mathematical Society
Page : 330 pages
File Size : 40,9 Mb
Release : 2023-02-22
Category : Mathematics
ISBN : 9781470468552

Get Book

Pick Interpolation and Hilbert Function Spaces by Jim Agler,John E. McCarthy Pdf

The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.

Theory of Function Spaces

Hans Triebel
Theory of Function Spaces Book PDF

Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 42,5 Mb
Release : 2010-08-20
Category : Science
ISBN : 9783034604154

Get Book

Theory of Function Spaces by Hans Triebel Pdf

The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where ‐∞s∞ and 0p,q≤∞, which include many classical and modern spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rsubn

A Primer on the Dirichlet Space

Anonim
A Primer on the Dirichlet Space Book PDF

Author : Anonim
Publisher : Unknown
Page : 228 pages
File Size : 49,7 Mb
Release : 2014
Category : Dirichlet principle
ISBN : 1139895109

Get Book

A Primer on the Dirichlet Space by Anonim Pdf

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 uniqu.

Theory of Function Spaces III

Hans Triebel
Theory of Function Spaces III Book PDF

Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 45,8 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9783764375829

Get Book

Theory of Function Spaces III by Hans Triebel Pdf

This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.

Spaces of Holomorphic Functions in the Unit Ball

Kehe Zhu
Spaces of Holomorphic Functions in the Unit Ball Book PDF

Author : Kehe Zhu
Publisher : Springer
Page : 0 pages
File Size : 55,8 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387501398

Get Book

Spaces of Holomorphic Functions in the Unit Ball by Kehe Zhu Pdf

Can be used as a graduate text Contains many exercises Contains new results

Function Spaces and Potential Theory

David R. Adams,Lars I. Hedberg
Function Spaces and Potential Theory Book PDF

Author : David R. Adams,Lars I. Hedberg
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662032824

Get Book

Function Spaces and Potential Theory by David R. Adams,Lars I. Hedberg Pdf

"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

Around the Research of Vladimir Maz'ya I

Ari Laptev
Around the Research of Vladimir Maz ya I Book PDF

Author : Ari Laptev
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 54,7 Mb
Release : 2009-12-02
Category : Mathematics
ISBN : 9781441913418

Get Book

Around the Research of Vladimir Maz'ya I by Ari Laptev Pdf

The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.

Function Spaces

Krzysztof Jarosz
Function Spaces Book PDF

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 54,5 Mb
Release : 2003
Category : Function spaces
ISBN : 9780821832691

Get Book

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.

Function Spaces and Operators between them

José Bonet,David Jornet,Pablo Sevilla-Peris
Function Spaces and Operators between them Book PDF

Author : José Bonet,David Jornet,Pablo Sevilla-Peris
Publisher : Springer Nature
Page : 279 pages
File Size : 53,9 Mb
Release : 2023-11-29
Category : Mathematics
ISBN : 9783031416026

Get Book

Function Spaces and Operators between them by José Bonet,David Jornet,Pablo Sevilla-Peris Pdf

The aim of this work is to present, in a unified and reasonably self-contained way, certain aspects of functional analysis which are needed to treat function spaces whose topology is not derived from a single norm, their topological duals and operators between those spaces. We treat spaces of continuous, analytic and smooth functions as well as sequence spaces. Operators of differentiation, integration, composition, multiplication and partial differential operators between those spaces are studied. A brief introduction to Laurent Schwartz’s theory of distributions and to Lars Hörmander’s approach to linear partial differential operators is presented. The novelty of our approach lies mainly on two facts. First of all, we show all these topics together in an accessible way, stressing the connection between them. Second, we keep it always at a level that is accessible to beginners and young researchers. Moreover, parts of the book might be of interest for researchers in functional analysis and operator theory. Our aim is not to build and describe a whole, complete theory, but to serve as an introduction to some aspects that we believe are interesting. We wish to guide any reader that wishes to enter in some of these topics in their first steps. Our hope is that they learn interesting aspects of functional analysis and become interested to broaden their knowledge about function and sequence spaces and operators between them. The text is addressed to students at a master level, or even undergraduate at the last semesters, since only knowledge on real and complex analysis is assumed. We have intended to be as self-contained as possible, and wherever an external citation is needed, we try to be as precise as we can. Our aim is to be an introduction to topics in, or connected with, different aspects of functional analysis. Many of them are in some sense classical, but we tried to show a unified direct approach; some others are new. This is why parts of these lectures might be of some interest even for researchers in related areas of functional analysis or operator theory. There is a full chapter about transitive and mean ergodic operators on locally convex spaces. This material is new in book form. It is a novel approach and can be of interest for researchers in the area.