Acoustic and Electromagnetic Equations / Integral Representations for Harmonic Problems, Nedelec Jean-Claude
Автор: Axler Sheldon, Bourdon Paul, Wade Ramey Название: Harmonic Function Theory ISBN: 0387952187 ISBN-13(EAN): 9780387952185 Издательство: Springer Рейтинг: Цена: 7836 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of BocherВїs Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by email-supplements the text for readers who wish to explore harmonic function theory on a computer.
Описание: This work has arisen from lecture courses given by the authors on important topics within functional analysis. The authors, who are all leading researchers, give introductions to their subjects at a level ideal for beginning graduate students, and others interested in the subject. The collection has been carefully edited so as to form a coherent and accessible introduction to current research topics. The first chapter by Professor Dales introduces the general theory of Banach algebras, which serves as a background to the remaining material. Dr Willis then studies a centrally important Banach algebra, the group algebra of a locally compact group. The remaining chapters are devoted to Banach algebras of operators on Banach spaces: Professor Eschmeier gives all the background for the exciting topic of invariant subspaces of operators, and discusses some key open problems; Dr Laursen and Professor Aiena discuss local spectral theory for operators, leading into Fredholm theory.
Автор: Ross G. Pinsky Название: Positive Harmonic Functions and Diffusion ISBN: 0521059836 ISBN-13(EAN): 9780521059831 Издательство: Cambridge Academ Рейтинг: Цена: 8397 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.
Автор: Yitzhak Katznelson Название: An Introduction to Harmonic Analysis ISBN: 0521543592 ISBN-13(EAN): 9780521543590 Издательство: Cambridge Academ Рейтинг: Цена: 4370 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.
Автор: Hewitt Название: Abstract Harmonic Analysis ISBN: 3540583181 ISBN-13(EAN): 9783540583189 Издательство: Springer Рейтинг: Цена: 9404 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups. This work aims at giving a monographic presentation of abstract harmonic analysis. It offers a many-sided outlook and leads up to modern developments.
Описание: Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fields, and features fully-refereed, high-quality papers exploring new results and trends in spectral theory, mathematical physics, geometric function theory, and partial differential equations. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. Another shared research interest of the contributors of this volume lies in the area of applied harmonic analysis, where a new notion called chromatic derivatives has recently been introduced in communication engineering.
The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6, 2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional mathematician and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.
Описание: This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory.
Harmonic Analysis on Symmetric Spaces--General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces.
Van den Ban's introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass-Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley-Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals.
Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, Harmonic Analysis on Symmetric Spaces--General Plancherel Theorems provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required.
Описание: An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the co
Автор: Heil Название: Harmonic Analysis and Applications ISBN: 0817637788 ISBN-13(EAN): 9780817637781 Издательство: Springer Рейтинг: Цена: 15674 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A self-contained volume in honor of John J. Benedetto that examines a wide range of topics in harmonic analysis and related areas. The book provides an excellent reference and contains authoritative expositions that will be of lasting interest.
Автор: Hewitt Название: Abstract Harmonic Analysis ISBN: 0387941908 ISBN-13(EAN): 9780387941905 Издательство: Springer Рейтинг: Цена: 15674 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book is based on courses given by E. Hewitt at the University of Washington and the University of Uppsala. The book is intended to be readable by
students who have had basic graduate courses in real analysis, set-theoretic topology, and algebra.
That is, the reader should know elementary set theory, set-theoretic
topology, measure theory, and algebra. The book begins with preliminaries in notation and terminology, group theory, and topology. It continues with elements of the theory of topological
groups, the integration on locally compact spaces, and invariant functionals.
The book concludes with convolutions and group representations, and characters and duality of
locally compact Abelian groups.
Описание: This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The first part of the book contains many
important theorems on the regularity of minimizing harmonic maps by Schoen-Uhlenbeck, stationary harmonic maps between Riemannian manifolds in higher dimensions by Evans and
Bethuel, and weakly harmonic maps from Riemannian surfaces by Helein, as well as on the structure of a singular set of minimizing harmonic maps and stationary harmonic maps by
Simon and Lin.The second part of the book contains a systematic coverage of heat flow of harmonic maps that includes Eells-Sampson's theorem on global smooth solutions, Struwe's
almost regular solutions in dimension two, Sacks-Uhlenbeck's blow-up analysis in dimension two, Chen-Struwe's existence theorem on partially smooth solutions, and blow-up analysis in
higher dimensions by Lin and Wang. The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric
partial differential equations and geometric analysis.
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