Riesz Transforms And The Bellman Function Technique
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Riesz Transforms And The Bellman Function Technique
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Author : Oliver Dragičević
language : en
Publisher:
Release Date : 2003
Riesz Transforms And The Bellman Function Technique written by Oliver Dragičević and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Harmonic analysis categories.
In the first part we use the technique of averaging to give a sharp weighted estimate for the operator of convolution with $z^{-2}$ (the Ahlfors-Beurling operator) for an arbitrary $A_2$ weight. As an application we touch upon the theory of quasiconformal mappings on $\hat{\Cc}$. The Ahlfors-Beurling operator can be realized as a combination of second-order Riesz transforms. We prove a new Littlewood-Paley-type inequality which is the key to our result in the second part. As some of its consequences, we show that the scalar Riesz transforms and their vector analogues admit dimension free upper estimates of the norms when acting on $L^p({\mathbb R}^n)$ for arbitrary dimension $n$ and $p>1$. The essence of the proof is the utilization of the method of Bellman functions, which, requiring but few assumptions, appears to allow its application to other kinds of Riesz transforms. We present the proof of one such example - dimensionless boundedness of Riesz transforms on Gaussian spaces.
The Bellman Function Technique In Harmonic Analysis
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Author : Vasily Vasyunin
language : en
Publisher: Cambridge University Press
Release Date : 2020-08-06
The Bellman Function Technique In Harmonic Analysis written by Vasily Vasyunin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-06 with Mathematics categories.
A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.
Classical Fourier Analysis
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Author : Loukas Grafakos
language : en
Publisher: Springer
Release Date : 2014-11-17
Classical Fourier Analysis written by Loukas Grafakos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-17 with Mathematics categories.
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.
New Trends In Applied Harmonic Analysis Volume 2
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Author : Akram Aldroubi
language : en
Publisher: Springer Nature
Release Date : 2019-11-26
New Trends In Applied Harmonic Analysis Volume 2 written by Akram Aldroubi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.
This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.
Gaussian Harmonic Analysis
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Author : Wilfredo Urbina-Romero
language : en
Publisher: Springer
Release Date : 2019-06-21
Gaussian Harmonic Analysis written by Wilfredo Urbina-Romero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-21 with Mathematics categories.
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.
Excursions In Harmonic Analysis Volume 2
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Author : Travis D Andrews
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-04
Excursions In Harmonic Analysis Volume 2 written by Travis D Andrews and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-04 with Mathematics categories.
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.
50 Years With Hardy Spaces
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Author : Anton Baranov
language : en
Publisher: Birkhäuser
Release Date : 2018-03-28
50 Years With Hardy Spaces written by Anton Baranov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-28 with Mathematics categories.
Written in honor of Victor Havin (1933–2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linköping University, are also included.
Analysis In Banach Spaces
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Author : Tuomas Hytönen
language : en
Publisher: Springer Nature
Release Date : 2024-01-08
Analysis In Banach Spaces written by Tuomas Hytönen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-08 with Mathematics categories.
This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 2003
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Dissertations, Academic categories.
Issues In General And Specialized Mathematics Research 2011 Edition
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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2012-01-09
Issues In General And Specialized Mathematics Research 2011 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-09 with Mathematics categories.
Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.