Îïèñàíèå: 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.

Îïèñàíèå: 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.

Àâòîð: Vladimir Britanak Íàçâàíèå: Discrete Cosine and Sine Transforms, ISBN: 0123736242 ISBN-13(EAN): 9780123736246 Èçäàòåëüñòâî: Elsevier Science Ðåéòèíã: Öåíà: 26730 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Presents the complete set of Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Loeve transform (KLT), with the emphasis on fast algorithms and integer approximations of DCTs and DSTs.

Àâòîð: Davies Brian Íàçâàíèå: Integral Transforms and Their Applications ISBN: 0387953140 ISBN-13(EAN): 9780387953144 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 17819 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: This book is an introduction and reference for the applications of integral transforms to a wide range of common mathematical problems. Emphasis is placed on the development of techniques and on the connection between properties of transforms and the kinds of problems for which they provide tools. Over 400 problems accompany the text, illustrating areas of applications. This third edition has been substantially updated, extended, and reorganized. Graduate students and researchers working in mathematics and physics will find this book useful.

Àâòîð: Fred King Íàçâàíèå: Hilbert Transforms ISBN: 0521887623 ISBN-13(EAN): 9780521887625 Èçäàòåëüñòâî: Cambridge Academ Ðåéòèíã: Öåíà: 22778 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications.

Íàçâàíèå: Guide to distribution theory and fourier transforms, a ISBN: 9812384308 ISBN-13(EAN): 9789812384300 Èçäàòåëüñòâî: World Scientific Publishing Ðåéòèíã: Öåíà: 8316 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Providing a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations, this book
clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many
problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals.

Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the
concepts in the book.

Íàçâàíèå: Guide to distribution theory and fourier transforms, a ISBN: 9812384219 ISBN-13(EAN): 9789812384218 Èçäàòåëüñòâî: World Scientific Publishing Ðåéòèíã: Öåíà: 8496 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: Providing a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations, this book
clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many
problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals.

Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the
concepts in the book.

Îïèñàíèå: This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms.

Àâòîð: King, Frederick W. Íàçâàíèå: Hilbert transforms ISBN: 0521517206 ISBN-13(EAN): 9780521517201 Èçäàòåëüñòâî: Cambridge Academ Ðåéòèíã: Öåíà: 27478 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications.

Àâòîð: R. J. Beerends Íàçâàíèå: Fourier and Laplace Transforms ISBN: 0521534410 ISBN-13(EAN): 9780521534413 Èçäàòåëüñòâî: Cambridge Academ Ðåéòèíã: Öåíà: 11929 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.

Îïèñàíèå: This tract gives a clear exposition of the elementary theory of Fourier transforms.

Àâòîð: Helgason Íàçâàíèå: Integral Geometry and Radon Transforms ISBN: 1441960546 ISBN-13(EAN): 9781441960542 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 11879 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.

Îïèñàíèå: In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University