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Author : J. J. Benedetto
Publisher : Springer
Page : 185 pages
File Size : 40,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540386025
Author : American Mathematical Society
Publisher : American Mathematical Soc.
Page : 438 pages
File Size : 43,9 Mb
Release : 1979
Category : Generalized spaces
ISBN : 9780821814383
Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, Lie groups and functional analysis
Author : John J. Benedetto
Publisher : Unknown
Page : 177 pages
File Size : 54,7 Mb
Release : 1980
Category : Electronic
ISBN : LCCN:80011359
Author : Elias M. Stein,Guido Weiss
Publisher : Princeton University Press
Page : 312 pages
File Size : 48,5 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883899
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Author : J. J. Benedetto
Publisher : Unknown
Page : 184 pages
File Size : 54,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662178176
Author : Guido L. Weiss,Stephen Wainger,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 492 pages
File Size : 41,6 Mb
Release : 1979-12-31
Category : Mathematics
ISBN : 0821867946
Contains sections on Real harmonic analysis, Hardy spaces and BMO,Harmonic functions, potential theory and theory of functions of one complex variable
Author : Guido Weiss,Stephen Wainger
Publisher : American Mathematical Soc.
Page : 452 pages
File Size : 47,7 Mb
Release : 1979-12-31
Category : Electronic
ISBN : 0821867954
Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, Lie groups and functional analysis
Author : Audrey Terras
Publisher : Springer Science & Business Media
Page : 413 pages
File Size : 40,6 Mb
Release : 2013-09-12
Category : Mathematics
ISBN : 9781461479727
This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups Γ, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.
Author : Steven G. Krantz
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 51,9 Mb
Release : 2019-07-03
Category : Electronic
ISBN : 9781470451127
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,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 510 pages
File Size : 42,9 Mb
Release : 2017-08-09
Category : Mathematics
ISBN : 9783319555560
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 : Guido Weiss,Stephen Wainger
Publisher : Unknown
Page : 438 pages
File Size : 54,5 Mb
Release : 1979
Category : Electronic
ISBN : OCLC:836686496
Author : Massimo Picardello
Publisher : CRC Press
Page : 180 pages
File Size : 50,8 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9781482285697
Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture
Author : Audrey Terras
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251286
Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.
Author : Camil Muscalu,Wilhelm Schlag
Publisher : Cambridge University Press
Page : 341 pages
File Size : 50,6 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781107031821
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217725
The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.