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Author : Leonard Gross
Publisher : American Mathematical Soc.
ISBN 13 : 0821812467
Total Pages : 67 pages
Book Rating : 4.8/5 (218 download)
Download or read book Harmonic Analysis on Hilbert Space written by Leonard Gross and published by American Mathematical Soc.. This book was released on 1963 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Béla Sz Nagy
Publisher : Springer Science & Business Media
ISBN 13 : 1441960937
Total Pages : 481 pages
Book Rating : 4.4/5 (419 download)
Download or read book Harmonic Analysis of Operators on Hilbert Space written by Béla Sz Nagy and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Author : B. La Sz -Nagy
Publisher :
ISBN 13 : 9781441960955
Total Pages : 490 pages
Book Rating : 4.9/5 (69 download)
Download or read book Harmonic Analysis of Operators on Hilbert Space written by B. La Sz -Nagy and published by . This book was released on 2011-02-18 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : B. Sz.-nagy
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)
Download or read book Harmonic Analysis of Operators on Hilbert Space written by B. Sz.-nagy and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. M. Gel'fand
Publisher : Academic Press
ISBN 13 : 1483262243
Total Pages : 399 pages
Book Rating : 4.4/5 (832 download)
Download or read book Generalized Functions written by I. M. Gel'fand and published by Academic Press. This book was released on 2014-05-12 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.
Author : Leonard Gross (wiskunde.)
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.:/5 (898 download)
Download or read book Harmonic Analysis on Hilbert Space written by Leonard Gross (wiskunde.) and published by . This book was released on 1963 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gerrit van Dijk
Publisher : Walter de Gruyter
ISBN 13 : 3110220202
Total Pages : 234 pages
Book Rating : 4.1/5 (12 download)
Download or read book Introduction to Harmonic Analysis and Generalized Gelfand Pairs written by Gerrit van Dijk and published by Walter de Gruyter. This book was released on 2009-12-23 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs
Author : Steven G. Krantz
Publisher : American Mathematical Soc.
ISBN 13 : 1470451123
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Panorama of Harmonic Analysis written by Steven G. Krantz and published by American Mathematical Soc.. This book was released on 2019-07-03 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 512 pages
Book Rating : 4.3/5 (195 download)
Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
Author : Carl L. DeVito
Publisher : Jones & Bartlett Learning
ISBN 13 : 9780763738938
Total Pages : 240 pages
Book Rating : 4.7/5 (389 download)
Download or read book Harmonic Analysis written by Carl L. DeVito and published by Jones & Bartlett Learning. This book was released on 2007 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Mathematics
Author : Roger Godement
Publisher : Springer
ISBN 13 : 3319169076
Total Pages : 535 pages
Book Rating : 4.3/5 (191 download)
Download or read book Analysis IV written by Roger Godement and published by Springer. This book was released on 2015-04-30 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.
Author : Béla Szőkefalvi-Nagy
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (844 download)
Download or read book Harmonic analysis of operators on Hilbert space, by B.Sz.-Nagy and C. Foias written by Béla Szőkefalvi-Nagy and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C. van den Berg
Publisher : Springer Science & Business Media
ISBN 13 : 146121128X
Total Pages : 299 pages
Book Rating : 4.4/5 (612 download)
Download or read book Harmonic Analysis on Semigroups written by C. van den Berg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk» is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.
Author : Christopher Heil
Publisher : Springer Science & Business Media
ISBN 13 : 0817645047
Total Pages : 390 pages
Book Rating : 4.8/5 (176 download)
Download or read book Harmonic Analysis and Applications written by Christopher Heil and published by Springer Science & Business Media. This book was released on 2007-08-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.
Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555502
Total Pages : 437 pages
Book Rating : 4.3/5 (195 download)
Download or read book Frames and Other Bases in Abstract and Function Spaces written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-06-11 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.
Author : Steven G. Krantz
Publisher : Springer Science & Business Media
ISBN 13 : 0817646698
Total Pages : 367 pages
Book Rating : 4.8/5 (176 download)
Download or read book Explorations in Harmonic Analysis written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2009-05-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Author : Maurice A. de Gosson
Publisher : Springer Science & Business Media
ISBN 13 : 3764399929
Total Pages : 351 pages
Book Rating : 4.7/5 (643 download)
Download or read book Symplectic Methods in Harmonic Analysis and in Mathematical Physics written by Maurice A. de Gosson and published by Springer Science & Business Media. This book was released on 2011-07-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
