Extremal Problems In Interpolation Theory Whitney Besicovitch Coverings And Singular Integrals
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Extremal Problems In Interpolation Theory Whitney Besicovitch Coverings And Singular Integrals
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Author : Sergey Kislyakov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-29
Extremal Problems In Interpolation Theory Whitney Besicovitch Coverings And Singular Integrals written by Sergey Kislyakov 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 2012-10-29 with Mathematics categories.
In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. The constructions are based on far-reaching refinements of the classical Calderón–Zygmund decomposition. These new Calderón–Zygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical results established by Besicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of Calderón–Zygmund singular integral operators. The book is divided into two parts. While the new method is presented in great detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic. There we discuss the classical covering results mentioned above, various spectacular applications of the classical Calderón–Zygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quick introduction to such important topics as spaces of smooth functions or singular integrals.
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.
Bellman Function For Extremal Problems In Bmo Ii Evolution
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Author : Paata Ivanisvili
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
Bellman Function For Extremal Problems In Bmo Ii Evolution written by Paata Ivanisvili and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Bounded mean oscillation categories.
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.
Fractals In Probability And Analysis
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Author : Christopher J. Bishop
language : en
Publisher: Cambridge University Press
Release Date : 2017
Fractals In Probability And Analysis written by Christopher J. Bishop 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 2017 with Mathematics categories.
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Explorations In Harmonic Analysis
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-24
Explorations In Harmonic Analysis written by Steven G. Krantz 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 2009-05-24 with Mathematics categories.
This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
1988
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Author : I. J. Schoenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 1988-06
1988 written by I. J. Schoenberg 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 1988-06 with Mathematics categories.
These seleeta contain 761 of the more than 2600 pages of 1. J. Schoenberg's published articles. The selection made and the grouping in which the papers are presented here reflect most strongly Schoenberg's wishes. The first volume of these seleeta is drawn from Schoenberg's remarkable work on Number Theory, Positive Definite Functions and Metric Geometry, Real and Complex Analysis, and on the Landau Problem. Schoenberg's fundamental papers on Total Pos itivity and Variation Diminution, on P6lya Frequency functions and sequences, and on Splines, especially Cardinal Splines, make up the second volume. In addition, various commentaries have been provided. Lettered references in these refer to items listed alphabetically at the end of each commentary. Numbered references refer to the list of Schoenberg's publications to be found in each volume. Those included in these seleeta are starred. It has been an honor to have been entrusted with the editorial work for these seleeta. I am grateful to the writers of the various commentaries for their illuminating contributions and to Richard Askey for solid advice.
Mathematical Conversations
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Author : Robin Wilson
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Mathematical Conversations written by Robin Wilson 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 2001 with Mathematics categories.
Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.
The Random Projection Method
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Author : Santosh S. Vempala
language : en
Publisher: American Mathematical Soc.
Release Date : 2005-02-24
The Random Projection Method written by Santosh S. Vempala and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-24 with Mathematics categories.
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neighbor search, geometric clustering and efficient low-rank approximation. Motivated by the first two applications, an extension of random projection to the hypercube is developed here. Throughout the book, random projection is used as a way to understand, simplify and connect progress on these important and seemingly unrelated problems. The book is suitable for graduate students and research mathematicians interested in computational geometry.
The Structure Of The Real Line
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Author : Lev Bukovský
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-02
The Structure Of The Real Line written by Lev Bukovský 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 2011-03-02 with Mathematics categories.
The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, and descriptive set theory are revisited with the purpose of eliminating superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind set theory is shortly explained in the appendix. Each section contains a series of exercises with additional results.
The Monodromy Group
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Author : Henryk Zoladek
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-10
The Monodromy Group written by Henryk Zoladek 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 2006-08-10 with Mathematics categories.
In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. There is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. In covering these and other topics, this book underlines the unifying role of the monogropy group.