Download or read book Harmonic Analysis at Mount Holyoke written by William Beckner and published by American Mathematical Soc.. This book was released on 2003 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on harmonic analysis and related areas. The conference provided an opportunity for researchers and students to exchange ideas and report on progress in this large and central field of modern mathematics. The volume is suitable for graduate students and research mathematicians interested in harmonic analysis and related areas.
Download or read book Discrete Analogues in Harmonic Analysis written by Ben Krause and published by American Mathematical Society. This book was released on 2023-01-19 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This timely book explores certain modern topics and connections at the interface of harmonic analysis, ergodic theory, number theory, and additive combinatorics. The main ideas were pioneered by Bourgain and Stein, motivated by questions involving averages over polynomial sequences, but the subject has grown significantly over the last 30 years, through the work of many researchers, and has steadily become one of the most dynamic areas of modern harmonic analysis. The author has succeeded admirably in choosing and presenting a large number of ideas in a mostly self-contained and exciting monograph that reflects his interesting personal perspective and expertise into these topics. —Alexandru Ionescu, Princeton University Discrete harmonic analysis is a rapidly developing field of mathematics that fuses together classical Fourier analysis, probability theory, ergodic theory, analytic number theory, and additive combinatorics in new and interesting ways. While one can find good treatments of each of these individual ingredients from other sources, to my knowledge this is the first text that treats the subject of discrete harmonic analysis holistically. The presentation is highly accessible and suitable for students with an introductory graduate knowledge of analysis, with many of the basic techniques explained first in simple contexts and with informal intuitions before being applied to more complicated problems; it will be a useful resource for practitioners in this field of all levels. —Terence Tao, University of California, Los Angeles
Download or read book Harmonic Analysis on the Real Line written by Elijah Liflyand and published by Springer Nature. This book was released on 2021-09-27 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.
Download or read book Fourier Analysis in Convex Geometry written by Alexander Koldobsky and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.
Download or read book Fourier Analysis and Convexity written by Luca Brandolini and published by Springer Science & Business Media. This book was released on 2011-04-27 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such as geometry, number theory, and analysis Contributors are leading experts in their respective fields Will be of interest to both pure and applied mathematicians
Download or read book Functional Analysis in Interdisciplinary Applications written by Tynysbek Sh. Kalmenov and published by Springer. This book was released on 2017-12-12 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents current research in functional analysis and its applications to a variety of problems in mathematics and mathematical physics. The book contains over forty carefully refereed contributions to the conference “Functional Analysis in Interdisciplinary Applications” (Astana, Kazakhstan, October 2017). Topics covered include the theory of functions and functional spaces; differential equations and boundary value problems; the relationship between differential equations, integral operators and spectral theory; and mathematical methods in physical sciences. Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis.
Download or read book Affine Density in Wavelet Analysis written by Gitta Kutyniok and published by Springer Science & Business Media. This book was released on 2007-07-12 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a thorough and comprehensive treatment of irregular wavelet frames. It introduces and employs a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Coverage includes non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
Download or read book Wave Packet Analysis written by Christoph Thiele and published by American Mathematical Soc.. This book was released on with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of ''wave packet analysis'' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L2$ functions. It was later used by Lacey and Thiele to prove bounds on the bilinear Hilbert transform. For quite some time, Carleson's wave packet analysis was thought to be an important idea, but that it had limited applications. But in recent years, it has become clear that this is an important tool for a number of other applications. This book isan introduction to these tools. It emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development. However, the book closes with a dedicated chapter on more recent results. Carleson's original theorem is sometimes cited as one of the most importantdevelopments of 20th century harmonic analysis. The set of ideas stemming from his proof is now seen as an essential element in modern harmonic analysis. Indeed, Thiele won the Salem prize jointly with Michael Lacey for work in this area. The book gives a nice survey of important material, such as an overview of the theory of singular integrals and wave packet analysis itself. There is a separate chapter on ''further developments'', which gives a broader view on the subject, though it does notexhaust all ongoing developments.
Download or read book Waves in Periodic and Random Media written by Peter Kuchment and published by American Mathematical Soc.. This book was released on 2003 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure. This book contains the proceedings of the research conference, ``Waves in Periodic and Random Media''. Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.
Download or read book Harmonic Analysis Partial Differential Equations and Applications written by Sagun Chanillo and published by Birkhäuser. This book was released on 2017-02-20 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.
Download or read book Fast Algorithms for Structured Matrices written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on 2003 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.
Download or read book Theory of Besov Spaces written by Yoshihiro Sawano and published by Springer. This book was released on 2018-11-04 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.
Download or read book Nonlinear Potential Theory on Metric Spaces written by Anders Björn and published by European Mathematical Society. This book was released on 2011 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Download or read book Decay of the Fourier Transform written by Alex Iosevich and published by Springer. This book was released on 2014-10-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Download or read book On a Conjecture of E M Stein on the Hilbert Transform on Vector Fields written by Michael Thoreau Lacey and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 205, number 965 (fourth of 5 numbers)."
Download or read book Stratified Lie Groups and Potential Theory for Their Sub Laplacians written by Andrea Bonfiglioli and published by Springer Science & Business Media. This book was released on 2007-08-24 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt:
