Gaussian Harmonic Analysis
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Gaussian Harmonic Analysis
Author | : Wilfredo Urbina-Romero |
Publsiher | : Springer |
Total Pages | : 477 |
Release | : 2019-06-21 |
Genre | : Mathematics |
ISBN | : 9783030055974 |
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Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading. Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.
Harmonic Analysis and the Theory of Probability
Author | : Saloman Bochner |
Publsiher | : Univ of California Press |
Total Pages | : 184 |
Release | : 2022-08-19 |
Genre | : Mathematics |
ISBN | : 9780520345287 |
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This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Twentieth Century Harmonic Analysis
Author | : J.S. Byrnes |
Publsiher | : Springer Science & Business Media |
Total Pages | : 411 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9789401006620 |
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Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated. The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.
Random Fourier Series with Applications to Harmonic Analysis
Author | : Michael B. Marcus,Gilles Pisier |
Publsiher | : Princeton University Press |
Total Pages | : 164 |
Release | : 1981-11-21 |
Genre | : Mathematics |
ISBN | : 0691082928 |
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The changes to U.S. immigration law that were instituted in 1965 have led to an influx of West African immigrants to New York, creating an enclave Harlem residents now call ''Little Africa.'' These immigrants are immediately recognizable as African in their wide-sleeved robes and tasseled hats, but most native-born members of the community are unaware of the crucial role Islam plays in immigrants' lives. Zain Abdullah takes us inside the lives of these new immigrants and shows how they deal with being a double minority in a country where both blacks and Muslims are stigmatized. Dealing with this dual identity, Abdullah discovers, is extraordinarily complex. Some longtime residents embrace these immigrants and see their arrival as an opportunity to reclaim their African heritage, while others see the immigrants as scornful invaders. In turn, African immigrants often take a particularly harsh view of their new neighbors, buying into the worst stereotypes about American-born blacks being lazy and incorrigible. And while there has long been a large Muslim presence in Harlem, and residents often see Islam as a force for social good, African-born Muslims see their Islamic identity disregarded by most of their neighbors. Abdullah weaves together the stories of these African Muslims to paint a fascinating portrait of a community's efforts to carve out space for itself in a new country. -- Book jacket.
Harmonic Analysis in Phase Space AM 122 Volume 122
Author | : Gerald B. Folland |
Publsiher | : Princeton University Press |
Total Pages | : 288 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 9781400882427 |
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This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.
Landscapes of Time Frequency Analysis
Author | : Paolo Boggiatto,Elena Cordero,Maurice de Gosson,Hans G. Feichtinger,Fabio Nicola,Alessandro Oliaro,Anita Tabacco |
Publsiher | : Springer |
Total Pages | : 358 |
Release | : 2019-01-30 |
Genre | : Mathematics |
ISBN | : 9783030052102 |
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The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include: Abstract harmonic analysis, Numerical harmonic analysis, Sampling theory, Compressed sensing, Mathematical signal processing, Pseudodifferential operators, and Applications of harmonic analysis to quantum mechanics. Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
Harmonic Analysis
Author | : María Cristina Pereyra,Lesley A. Ward |
Publsiher | : American Mathematical Soc. |
Total Pages | : 437 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9780821875667 |
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Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).
Excursions in Harmonic Analysis Volume 2
Author | : Travis D Andrews,Radu Balan,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou |
Publsiher | : Springer Science & Business Media |
Total Pages | : 461 |
Release | : 2013-01-04 |
Genre | : Mathematics |
ISBN | : 9780817683795 |
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The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis. This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts: Volume I · Sampling Theory · Remote Sensing · Mathematics of Data Processing · Applications of Data Processing Volume II · Measure Theory · Filtering · Operator Theory · Biomathematics Each part provides state-of-the-art results, with contributions from an impressive array of mathematicians, engineers, and scientists in academia, industry, and government. Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.