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Author : Vasily Vasyunin,Alexander Volberg
Publisher : Cambridge University Press
Page : 465 pages
File Size : 49,7 Mb
Release : 2020-08-06
Category : Mathematics
ISBN : 9781108486897
A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.
Author : Alexander Koldobsky,Alexander Volberg
Publisher : Walter de Gruyter GmbH & Co KG
Page : 608 pages
File Size : 42,8 Mb
Release : 2023-07-24
Category : Mathematics
ISBN : 9783110775433
In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.
Author : Patricio Cifuentes,José García-Cuerva,Gustavo Garrigós, Eugenio Hernández,José María Martell,Javier Parcet,Keith M. Rogers,Alberto Ruiz,Fernando Soria,Ana Vargas
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 41,6 Mb
Release : 2013-12-06
Category : Mathematics
ISBN : 9780821894330
This volume contains the Proceedings of the 9th International Conference on Harmonic Analysis and Partial Differential Equations, held June 11-15, 2012, in El Escorial, Madrid, Spain. Included in this volume is the written version of the mini-course given by Jonathan Bennett on Aspects of Multilinear Harmonic Analysis Related to Transversality. Also included, among other papers, is a paper by Emmanouil Milakis, Jill Pipher, and Tatiana Toro, which reflects and extends the ideas presented in the mini-course on Analysis on Non-smooth Domains delivered at the conference by Tatiana Toro. The topics of the contributed lectures cover a wide range of the field of Harmonic Analysis and Partial Differential Equations and illustrate the fruitful interplay between the two subfields.
Author : Travis D Andrews,Radu Balan,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 40,6 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 9780817683795
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.
Author : Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
Publisher : Springer Nature
Page : 335 pages
File Size : 43,6 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030323530
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.
Author : Ariel Yadin
Publisher : Cambridge University Press
Page : 404 pages
File Size : 55,7 Mb
Release : 2024-05-31
Category : Mathematics
ISBN : 9781009546577
Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet–Deny Theorem, the Milnor–Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.
Author : Paolo Ciatti,Alessio Martini
Publisher : Springer Nature
Page : 488 pages
File Size : 40,5 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030720582
This volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables. The work is addressed to researchers in the field.
Author : Paata Ivanisvili,Dmitriy M. Stolyarov,Vasily I. Vasyunin,Pavel B. Zatitskiy
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 49,6 Mb
Release : 2018-10-03
Category : Bounded mean oscillation
ISBN : 9781470429546
In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.
Author : Alberto Torchinsky
Publisher : Elsevier
Page : 474 pages
File Size : 49,5 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483268880
Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.
Author : Daomin Cao,Shuangjie Peng,Shusen Yan
Publisher : Cambridge University Press
Page : 263 pages
File Size : 44,8 Mb
Release : 2021-02-18
Category : Mathematics
ISBN : 9781108836838
A systematic introduction to the singularly perturbed methods in the study of concentration solutions for nonlinear elliptic problems.
Author : Oliver Dragičević
Publisher : Unknown
Page : 164 pages
File Size : 55,7 Mb
Release : 2003
Category : Harmonic analysis
ISBN : MSU:31293024553574
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.
Author : Joseph Rosenblatt
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 50,8 Mb
Release : 2007
Category : Ergodic theory
ISBN : 9780821842355
There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. This text presents a series of essays on the topic.
Author : Adam Sheffer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 55,6 Mb
Release : 2022-03-24
Category : Mathematics
ISBN : 9781108832496
A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
Author : Félix Cabello Sánchez,Jesús M. F. Castillo
Publisher : Cambridge University Press
Page : 562 pages
File Size : 51,8 Mb
Release : 2023-01-31
Category : Mathematics
ISBN : 9781108807883
Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.
Author : Jan van Neerven
Publisher : Cambridge University Press
Page : 728 pages
File Size : 51,6 Mb
Release : 2022-07-07
Category : Mathematics
ISBN : 9781009232494
This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.
