Download or read book Function Spaces and Potential Theory written by David R. Adams and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: "..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
Download or read book From Vector Spaces to Function Spaces written by Yutaka Yamamoto and published by SIAM. This book was released on 2012-10-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.
Download or read book Linear Processes in Function Spaces written by Denis Bosq and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.
Download or read book Function Theory and p Spaces written by Raymond Cheng and published by American Mathematical Soc.. This book was released on 2020-05-28 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Analysis and Function Spaces written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.
Download or read book Theory of Function Spaces II written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2010-05-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Function Spaces IV written by Hans Triebel and published by Springer Nature. This book was released on 2020-01-23 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".
Download or read book Function Spaces 1 written by Luboš Pick and published by Walter de Gruyter. This book was released on 2012-12-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Integral Operators in Non Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Download or read book Function Spaces and Applications written by Michael Cwikel and published by Springer. This book was released on 2006-11-15 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This seminar is a loose continuation of two previous conferences held in Lund (1982, 1983), mainly devoted to interpolation spaces, which resulted in the publication of the Lecture Notes in Mathematics Vol. 1070. This explains the bias towards that subject. The idea this time was, however, to bring together mathematicians also from other related areas of analysis. To emphasize the historical roots of the subject, the collection is preceded by a lecture on the life of Marcel Riesz.
Download or read book Optimization in Function Spaces written by Amol Sasane and published by Courier Dover Publications. This book was released on 2016-03-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classroom-tested at the London School of Economics, this original, highly readable text offers numerous examples and exercises as well as detailed solutions. Prerequisites are multivariable calculus and basic linear algebra. 2015 edition.
Download or read book The Dirichlet Space and Related Function Spaces written by Nicola Arcozzi and published by American Mathematical Soc.. This book was released on 2019-09-03 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Function Spaces written by Krzysztof Jarosz and published by American Mathematical Soc.. This book was released on 2007 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.
Download or read book Maximal Function Methods for Sobolev Spaces written by Juha Kinnunen and published by American Mathematical Soc.. This book was released on 2021-08-02 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Society. This book was released on 2023-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Functional Spaces for the Theory of Elliptic Partial Differential Equations written by Françoise Demengel and published by Springer Science & Business Media. This book was released on 2012-01-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
Download or read book Function Spaces written by Krzysztof Jarov and published by CRC Press. This book was released on 2020-08-27 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the conference on Function Spaces held at Southern Illinois University at Edwardsville, in April, 1990. It is designed to cover a wide range of topics, including spaces of analytic functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.
