Topics In Harmonic Analysis Related To The Littlewood Paley Theory Am 63 Volume 63
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| Author | : Feng Dai |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 447 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1461466601 |
This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
| Author | : Björn Böttcher |
| Publisher | : Springer |
| Total Pages | : 215 |
| Release | : 2014-01-16 |
| Genre | : Mathematics |
| ISBN | : 3319026844 |
This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is a counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.
| Author | : Catherine Donati-Martin |
| Publisher | : Springer |
| Total Pages | : 511 |
| Release | : 2014-12-29 |
| Genre | : Mathematics |
| ISBN | : 3319119702 |
Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.
| Author | : Robion C. Kirby |
| Publisher | : Princeton University Press |
| Total Pages | : 368 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400881501 |
Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
| Author | : Guido Weiss |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 448 |
| Release | : 1979 |
| Genre | : Mathematics |
| ISBN | : 0821814389 |
Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, and Lie groups and functional analysis.
| Author | : William B. Johnson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 306 |
| Release | : 1979 |
| Genre | : Mathematics |
| ISBN | : 0821822179 |
In this paper detailed investigations of spaces with a symmetric basis of finite length and rearrangement invariant function spaces are presented. The emphasis is on questions arising naturally from the theory of [italic]L[italic subscript]p-spaces.
| Author | : María Cristina Pereyra |
| Publisher | : Springer |
| Total Pages | : 469 |
| Release | : 2017-07-10 |
| Genre | : Mathematics |
| ISBN | : 3319515934 |
This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic harmonic analysis. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. A survey of the two weight problem for the Hilbert transform and an expository article on the Clark model to the case of non-singular measures and applications to the study of rank-one perturbations are included. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6,2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional scientist and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.
| Author | : John Frank Adams |
| Publisher | : Princeton University Press |
| Total Pages | : 230 |
| Release | : 1978-09-01 |
| Genre | : Mathematics |
| ISBN | : 1400821258 |
The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.
| Author | : Elias M. Stein |
| Publisher | : Princeton University Press |
| Total Pages | : 160 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400881870 |
This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.
| Author | : Brian Street |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 768 |
| Release | : 2023-07-03 |
| Genre | : Mathematics |
| ISBN | : 3111085643 |
Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.
