Download or read book Lectures on Hermite and Laguerre Expansions MN 42 Volume 42 written by Sundaram Thangavelu and published by Princeton University Press. This book was released on 2020-06-16 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.

Download or read book Lectures on Hermite and Laguerre Expansions written by Sundaram Thangavelu and published by Princeton University Press. This book was released on 1993-05-09 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.

Download or read book Recent Developments in Real and Harmonic Analysis written by Carlos Cabrelli and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis. The work begins with a chronological description of Segovia’s mathematical life, highlighting his original ideas and their evolution. Also included are surveys dealing with Carlos’ favorite topics, and PDE works written by students and colleagues close to Segovia whose careers were in some way influenced by him. Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, C.E. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea.

Download or read book Harmonic Analysis written by J. Marshall Ash and published by American Mathematical Soc.. This book was released on 2006 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting in the early 1950's, Alberto Calderon, Antoni Zygmund, and their students developed a program in harmonic analysis with far-reaching consequences. The title of these proceedings reflects this broad reach. This book came out of a DePaul University conference honoring Stephen Vagi upon his retirement in 2002. Vagi was a student of Calderon in the 1960's, when Calderon and Zygmund were at their peak. Two authors, Kenig and Gatto, were students of Calderon; one, Muckenhoupt, was a student of Zygmund. Two others studied under Zygmund's student Elias Stein. The remaining authors all have close connections with the Calderon-Zygmund school of analysis. This book should interest specialists in harmonic analysis and those curious to see it applied to partial differential equations and ergodic theory. In the first article, Adam Koranyi summarizes Vagi's work. Four additional articles cover various recent developments in harmonic analysis: Eduardo Gatto studies spaces with doubling and non-doubling measures; Cora Sadosky, product spaces; Benjamin Muckenhoupt, Laguerre expansions; and Roger Jones, singular integrals. Charles Fefferman and Carlos Kenig present applications to partial differential equations and Stephen Wainger gives an application to ergodic theory. The final article records some interesting open questions from a problem session that concluded the conference.

Download or read book Advanced Courses Of Mathematical Analysis Vi Proceedings Of The Sixth International School written by Francisco Javier Martin-reyes and published by World Scientific. This book was released on 2016-10-27 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains short courses and recent papers by several specialists in different fields of Mathematical Analysis. It offers a wide perspective of the current state of research, and new trends, in areas related to Geometric Analysis, Harmonic Analysis, Complex Analysis, Functional Analysis and History of Mathematics. The contributions are presented with a remarkable expository nature and this makes the discussed topics accessible to a more general audience.

Download or read book Laguerre Calculus and Its Applications on the Heisenberg Group written by Carlos A. Berenstein and published by American Mathematical Soc.. This book was released on 2001 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: For nearly two centuries, the relation between analytic functions of one complex variable, their boundary values, harmonic functions, and the theory of Fourier series has been one of the central topics of study in mathematics. The topic stands on its own, yet also provides very useful mathematical applications. This text provides a self-contained introduction to the corresponding questions in several complex variables: namely, analysis on the Heisenberg group and the study of the solutions of the boundary Cauchy-Riemann equations. In studying this material, readers are exposed to analysis in non-commutative compact and Lie groups, specifically the rotation group and the Heisenberg groups-both fundamental in the theory of group representations and physics. Introduced in a concrete setting are the main ideas of the Calderón-Zygmund-Stein school of harmonic analysis. Also considered in the book are some less conventional problems of harmonic and complex analysis, in particular, the Morera and Pompeiu problems for the Heisenberg group, which relates to questions in optics, tomography, and engineering. The book was borne of graduate courses and seminars held at the University of Maryland (College Park), the University of Toronto (ON), Georgetown University (Washington, DC), and the University of Georgia (Athens). Readers should have an advanced undergraduate understanding of Fourier analysis and complex analysis in one variable.

Download or read book Analysis and Partial Differential Equations Perspectives from Developing Countries written by Julio Delgado and published by Springer. This book was released on 2019-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries. Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudo-differential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China. Suitable for postgraduate students and beyond, this volume offers the reader a broader, global perspective of contemporary research in analysis.

Download or read book Gaussian Harmonic Analysis written by Wilfredo Urbina-Romero and published by Springer. This book was released on 2019-06-21 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Special Functions and Orthogonal Polynomials written by Refaat El Attar and published by Lulu.com. This book was released on 2006 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: (308 Pages). This book is written to provide an easy to follow study on the subject of Special Functions and Orthogonal Polynomials. It is written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Special Functions and Orthogonal Polynomials that very often occur in engineering, physics, mathematics and applied sciences. The book is organized in chapters that are in a sense self contained. Chapter 1 deals with series solutions of Differential Equations. Gamma and Beta functions are studied in Chapter 2 together with other functions that are defined by integrals. Legendre Polynomials and Functions are studied in Chapter 3. Chapters 4 and 5 deal with Hermite, Laguerre and other Orthogonal Polynomials. A detailed treatise of Bessel Function in given in Chapter 6.

Download or read book Special Functions written by Refaat El Attar and published by Lulu.com. This book was released on 2005-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Hardcover). This book is written to provide an easy to follow study on the subject of Special Functions and Orthogonal Polynomials. It is written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Special Functions and Orthogonal Polynomials that very often occur in engineering, physics, mathematics and applied sciences. The book is organized in chapters that are in a sense self contained. Chapter 1 deals with series solutions of Differential Equations. Gamma and Beta functions are studied in Chapter 2 together with other functions that are defined by integrals. Legendre Polynomials and Functions are studied in Chapter 3. Chapters 4 and 5 deal with Hermite, Laguerre and other Orthogonal Polynomials. A detailed treatise of Bessel Function in given in Chapter 6.

Download or read book Radon Transforms Geometry and Wavelets written by Gestur Ólafsson and published by American Mathematical Soc.. This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on two special sessions held at the AMS Annual Meeting in New Orleans in January 2007, and a satellite workshop held in Baton Rouge on January 4-5, 2007. It consists of invited expositions that together represent a broad spectrum of fields, stressing surprising interactions and connections between areas that are normally thought of as disparate. The main topics are geometry and integral transforms. On the one side are harmonic analysis, symmetric spaces,representation theory (the groups include continuous and discrete, finite and infinite, compact and non-compact), operator theory, PDE, and mathematical probability. Moving in the applied direction we encounter wavelets, fractals, and engineering topics such as frames and signal and image processing.The subjects covered in this book form a unified whole, and they stand at the crossroads of pure and applied mathematics. The articles cover a broad range in harmonic analysis, with the main themes related to integral geometry, the Radon transform, wavelets and frame theory. These themes can loosely be grouped together as follows:Frame Theory and ApplicationsHarmonic Analysis and Function SpacesHarmonic Analysis and Number TheoryIntegral Geometry and Radon TransformsMultiresolution Analysis, Wavelets, and Applications

Download or read book Special Functions written by Nico M. Temme and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.

Download or read book Encyclopedia of Special Functions The Askey Bateman Project Volume 2 Multivariable Special Functions written by Tom H. Koornwinder and published by Cambridge University Press. This book was released on 2020-10-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Download or read book Analysis On Gaussian Spaces written by Yaozhong Hu and published by World Scientific. This book was released on 2016-08-30 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Written by a well-known expert in fractional stochastic calculus, this book offers a comprehensive overview of Gaussian analysis, with particular emphasis on nonlinear Gaussian functionals. In addition, it covers some topics that are not frequently encountered in other treatments, such as Littlewood-Paley-Stein, etc. This coverage makes the book a valuable addition to the literature. Many results presented in this book were hitherto available only in the research literature in the form of research papers by the author and his co-authors.'Mathematical Reviews ClippingsAnalysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is the Gaussian measure, which has been unified under the terminology of 'abstract Wiener space'.Out of the large amount of work on this topic, this book presents some fundamental results plus recent progress. We shall present some results on the Gaussian space itself such as the Brunn-Minkowski inequality, Small ball estimates, large tail estimates. The majority part of this book is devoted to the analysis of nonlinear functions on the Gaussian space. Derivative, Sobolev spaces are introduced, while the famous Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood-Paley-Stein-Meyer theory are given in details.This book includes some basic material that cannot be found elsewhere that the author believes should be an integral part of the subject. For example, the book includes some interesting and important inequalities, the Littlewood-Paley-Stein-Meyer theory, and the Hörmander theorem. The book also includes some recent progress achieved by the author and collaborators on density convergence, numerical solutions, local times.

Download or read book Extended Abstracts 2021 2022 written by Duván Cardona and published by Springer Nature. This book was released on with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Malliavin Calculus for L vy Processes with Applications to Finance written by Giulia Di Nunno and published by Springer Science & Business Media. This book was released on 2008-10-08 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

Download or read book Orthogonal Polynomials of Several Variables written by Charles F. Dunkl and published by Cambridge University Press. This book was released on 2001-02-22 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal polynomials of several variables, approximation theory, symmetry-group methods.