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

Sergey Kislyakov,Natan Kruglyak
Extremal Problems in Interpolation Theory Whitney Besicovitch Coverings and Singular Integrals Book PDF

Author : Sergey Kislyakov,Natan Kruglyak
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 54,8 Mb
Release : 2012-10-29
Category : Mathematics
ISBN : 9783034804691

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Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals by Sergey Kislyakov,Natan Kruglyak Pdf

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

Loukas Grafakos
Classical Fourier Analysis Book PDF

Author : Loukas Grafakos
Publisher : Springer
Page : 647 pages
File Size : 52,6 Mb
Release : 2014-11-17
Category : Mathematics
ISBN : 9781493911943

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Classical Fourier Analysis by Loukas Grafakos Pdf

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

Paata Ivanisvili,Dmitriy M. Stolyarov,Vasily I. Vasyunin,Pavel B. Zatitskiy
Bellman Function for Extremal Problems in BMO II Evolution Book PDF

Author : Paata Ivanisvili,Dmitriy M. Stolyarov,Vasily I. Vasyunin,Pavel B. Zatitskiy
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 49,7 Mb
Release : 2018-10-03
Category : Bounded mean oscillation
ISBN : 9781470429546

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Bellman Function for Extremal Problems in BMO II: Evolution by Paata Ivanisvili,Dmitriy M. Stolyarov,Vasily I. Vasyunin,Pavel B. Zatitskiy Pdf

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

Christopher J. Bishop,Yuval Peres
Fractals in Probability and Analysis Book PDF

Author : Christopher J. Bishop,Yuval Peres
Publisher : Cambridge University Press
Page : 415 pages
File Size : 48,7 Mb
Release : 2017
Category : Mathematics
ISBN : 9781107134119

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Fractals in Probability and Analysis by Christopher J. Bishop,Yuval Peres Pdf

A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Explorations in Harmonic Analysis

Steven G. Krantz
Explorations in Harmonic Analysis Book PDF

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 51,5 Mb
Release : 2009-05-24
Category : Mathematics
ISBN : 9780817646691

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Explorations in Harmonic Analysis by Steven G. Krantz Pdf

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.

The Random Projection Method

Santosh S. Vempala
The Random Projection Method Book PDF

Author : Santosh S. Vempala
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 42,5 Mb
Release : 2005-02-24
Category : Mathematics
ISBN : 9780821837931

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The Random Projection Method by Santosh S. Vempala Pdf

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.

(1988).

I. J. Schoenberg
1988 Book PDF

Author : I. J. Schoenberg
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 41,8 Mb
Release : 1988-06
Category : Mathematics
ISBN : 0817634045

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(1988). by I. J. Schoenberg Pdf

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

Robin Wilson,Jeremy Gray
Mathematical Conversations Book PDF

Author : Robin Wilson,Jeremy Gray
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 41,9 Mb
Release : 2001
Category : Mathematics
ISBN : 0387986863

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Mathematical Conversations by Robin Wilson,Jeremy Gray Pdf

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 Structure of the Real Line

Lev Bukovský
The Structure of the Real Line Book PDF

Author : Lev Bukovský
Publisher : Springer Science & Business Media
Page : 546 pages
File Size : 49,7 Mb
Release : 2011-03-02
Category : Mathematics
ISBN : 9783034800068

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The Structure of the Real Line by Lev Bukovský Pdf

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.

A First Course in Sobolev Spaces

Giovanni Leoni
A First Course in Sobolev Spaces Book PDF

Author : Giovanni Leoni
Publisher : American Mathematical Soc.
Page : 626 pages
File Size : 50,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847688

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A First Course in Sobolev Spaces by Giovanni Leoni Pdf

Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the book makes it suitable for advanced undergraduates or beginning graduate students. Moreover, the one-variable part of the book helps to develop a solid background that facilitates the reading and understanding of Sobolev functions of several variables. The second part of the book is more classical, although it also contains some recent results. Besides the standard results on Sobolev functions, this part of the book includes chapters on BV functions, symmetric rearrangement, and Besov spaces. The book contains over 200 exercises.

The Monodromy Group

Henryk Zoladek
The Monodromy Group Book PDF

Author : Henryk Zoladek
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 54,8 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9783764375362

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The Monodromy Group by Henryk Zoladek Pdf

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.

The Mathematics of Paul Erdös I

Ronald Lewis Graham,Jaroslav Nesetril
The Mathematics of Paul Erd s I Book PDF

Author : Ronald Lewis Graham,Jaroslav Nesetril
Publisher : Springer Science & Business Media
Page : 413 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642604089

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The Mathematics of Paul Erdös I by Ronald Lewis Graham,Jaroslav Nesetril Pdf

In 1992, when Paul Erdos was awarded a Doctor Honoris Causa by Charles University in Prague, a small conference was held, bringing together a distin guished group of researchers with interests spanning a variety of fields related to Erdos' own work. At that gathering, the idea occurred to several of us that it might be quite appropriate at this point in Erdos' career to solicit a col lection of articles illustrating various aspects of Erdos' mathematical life and work. The response to our solicitation was immediate and overwhelming, and these volumes are the result. Regarding the organization, we found it convenient to arrange the papers into six chapters, each mirroring Erdos' holistic approach to mathematics. Our goal was not merely a (random) collection of papers but rather a thor oughly edited volume composed in large part by articles explicitly solicited to illustrate interesting aspects of Erdos and his life and work. Each chap ter includes an introduction which often presents a sample of related ErdOs' problems "in his own words". All these (sometimes lengthy) introductions were written jointly by editors. We wish to thank the nearly 70 contributors for their outstanding efforts (and their patience). In particular, we are grateful to Bela Bollobas for his extensive documentation of Paul Erdos' early years and mathematical high points (in the first part of this volume); our other authors are acknowledged in their respective chapters. We also want to thank A. Bondy, G. Hahn, I.

Quasiconformal Mappings and Analysis

Peter Duren,Juha Heinonen,Brad Osgood,Bruce Palka
Quasiconformal Mappings and Analysis Book PDF

Author : Peter Duren,Juha Heinonen,Brad Osgood,Bruce Palka
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206057

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Quasiconformal Mappings and Analysis by Peter Duren,Juha Heinonen,Brad Osgood,Bruce Palka Pdf

In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.

Cardinal Spline Interpolation

I. J. Schoenberg
Cardinal Spline Interpolation Book PDF

Author : I. J. Schoenberg
Publisher : SIAM
Page : 127 pages
File Size : 48,6 Mb
Release : 1973-01-01
Category : Mathematics
ISBN : 9780898710090

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Cardinal Spline Interpolation by I. J. Schoenberg Pdf

In this book the author explains cardinal spline functions, the basic properties of B-splines and exponential Euler splines.

Orthopoxviruses Pathogenic for Humans

Anonim
Orthopoxviruses Pathogenic for Humans Book PDF

Author : Anonim
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 40,7 Mb
Release : 2006-06-09
Category : Medical
ISBN : 9780387253060

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Orthopoxviruses Pathogenic for Humans by Anonim Pdf

Orthopoxviruses Pathogenic for Humans covers those viruses capable of causing disease in man, including monkeypox, smallpox, cowpox, and vaccinia. The coverage of each virus is comprehensive, covering the biology, molecular biology, and ecology of the virus as well as the clinical and epidemiological aspects of these viruses in humans and animals. In addition, this volume highlights developments in genetic engineering that are paving the way for potential therapeutic treatments of these viruses.