• Mathematics

Classical and Multilinear Harmonic Analysis


Author: Camil Muscalu,Wilhelm Schlag
Publisher: Cambridge University Press
ISBN: 0521882451
Category: Mathematics
Page: 387
View: 8511
"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderâon-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderâon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"--

    • Mathematics

Classical and Multilinear Harmonic Analysis


Author: Camil Muscalu,Wilhelm Schlag
Publisher: Cambridge University Press
ISBN: 1107031826
Category: Mathematics
Page: 339
View: 9742
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

    • Mathematics

An Introduction to Harmonic Analysis


Author: Yitzhak Katznelson
Publisher: Cambridge University Press
ISBN: 9780521543590
Category: Mathematics
Page: 314
View: 2231
First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

    • Mathematics

Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems


Author: Carlos E. Kenig
Publisher: American Mathematical Soc.
ISBN: 0821803093
Category: Mathematics
Page: 146
View: 9601
In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.

    • Mathematics

Wave Packet Analysis


Author: Christoph Thiele
Publisher: American Mathematical Soc.
ISBN: 0821836617
Category: Mathematics
Page: 86
View: 8261
The concept of "wave packet analysis" originates in Carleson's famous proof of almost everywhere convergence of Fourier series of LÝsuperscript 2¨ 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 is an 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. 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 not exhaust all ongoing developments.

    • Mathematics

Classical Fourier Analysis


Author: Loukas Grafakos
Publisher: Springer
ISBN: 1493911945
Category: Mathematics
Page: 638
View: 4685
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.

    • Mathematics

Global Analysis

Differential Forms in Analysis, Geometry, and Physics
Author: Ilka Agricola,Thomas Friedrich
Publisher: American Mathematical Soc.
ISBN: 0821829513
Category: Mathematics
Page: 343
View: 5434
This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics. There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics.

    • Mathematics

Modern Fourier Analysis


Author: Loukas Grafakos
Publisher: Springer
ISBN: 1493912305
Category: Mathematics
Page: 624
View: 1806
This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary.

    • Mathematics

Twelve Landmarks of Twentieth-Century Analysis


Author: D. Choimet,H. Queffélec
Publisher: Cambridge University Press
ISBN: 1316352137
Category: Mathematics
Page: N.A
View: 3112
The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors' original approach combines rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into these landmarks in mathematics. Results ranging from the proof of Littlewood's conjecture to the Banach–Tarski paradox have been selected for their mathematical beauty as well as educative value and historical role. Placing each theorem in historical perspective, the authors paint a coherent picture of modern analysis and its development, whilst maintaining mathematical rigour with the provision of complete proofs, alternative proofs, worked examples, and more than 150 exercises and solution hints. This edition extends the original French edition of 2009 with a new chapter on partitions, including the Hardy–Ramanujan theorem, and a significant expansion of the existing chapter on the Corona problem.

    • Mathematics

Advances in Analysis

The Legacy of Elias M. Stein
Author: Charles Fefferman,Alexandru D. Ionescu,D.H. Phong,Stephen Wainger
Publisher: Princeton University Press
ISBN: 1400848938
Category: Mathematics
Page: 480
View: 5721
Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze-Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collaborators and students, Stein has changed mathematics. Drawing inspiration from Stein’s contributions to harmonic analysis and related topics, this volume gathers papers from internationally renowned mathematicians, many of whom have been Stein’s students. The book also includes expository papers on Stein’s work and its influence. The contributors are Jean Bourgain, Luis Caffarelli, Michael Christ, Guy David, Charles Fefferman, Alexandru D. Ionescu, David Jerison, Carlos Kenig, Sergiu Klainerman, Loredana Lanzani, Sanghyuk Lee, Lionel Levine, Akos Magyar, Detlef Müller, Camil Muscalu, Alexander Nagel, D. H. Phong, Malabika Pramanik, Andrew S. Raich, Fulvio Ricci, Keith M. Rogers, Andreas Seeger, Scott Sheffield, Luis Silvestre, Christopher D. Sogge, Jacob Sturm, Terence Tao, Christoph Thiele, Stephen Wainger, and Steven Zelditch.

    • Combinatorial geometry

Polynomial Methods in Combinatorics


Author: Larry Guth
Publisher: American Mathematical Soc.
ISBN: 1470428903
Category: Combinatorial geometry
Page: 273
View: 6018
This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.

    • Mathematics

Fourier Integrals in Classical Analysis


Author: Christopher D. Sogge
Publisher: Cambridge University Press
ISBN: 9780521434645
Category: Mathematics
Page: 236
View: 2534
An advanced monograph concerned with modern treatments of central problems in harmonic analysis.

    • Differential equations, Nonlinear

Harmonic Analysis Method for Nonlinear Evolution Equations, I


Author: Baoxiang Wang,Zhaohui Huo,Zihua Guo,Chengchun Hao
Publisher: World Scientific
ISBN: 9814360740
Category: Differential equations, Nonlinear
Page: 283
View: 5166
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear SchrAdinger equations, nonlinear KleinOCoGordon equations, KdV equations as well as NavierOCoStokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods. This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

    • Mathematics

Fourier Analysis on Finite Groups and Applications


Author: Audrey Terras
Publisher: Cambridge University Press
ISBN: 9780521457187
Category: Mathematics
Page: 442
View: 2254
A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.

    • Mathematics

Principles of Mathematical Analysis


Author: Walter Rudin
Publisher: McGraw-Hill Publishing Company
ISBN: 9780070856134
Category: Mathematics
Page: 342
View: 1703
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

    • Mathematics

Harmonic Analysis, Partial Differential Equations and Applications

In Honor of Richard L. Wheeden
Author: Sagun Chanillo,Bruno Franchi,Guozhen Lu,Carlos Perez,Eric T. Sawyer
Publisher: Birkhäuser
ISBN: 3319527428
Category: Mathematics
Page: 301
View: 1838
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.

    • Mathematics

Harmonic Approximation


Author: Stephen J. Gardiner
Publisher: Cambridge University Press
ISBN: 9780521497992
Category: Mathematics
Page: 132
View: 9386
Harmonic approximation has recently matured into a coherent research area with extensive applications. This is the first book to give a systematic account of these developments, beginning with classical results concerning uniform approximation on compact sets, and progressing through fusion techniques to deal with approximation on unbounded sets. The author draws inspiration from holomorphic results such as the well-known theorems of Runge and Mergelyan. The final two chapters deal with wide ranging and surprising applications to the Dirichlet problem, maximum principle, Radon transform and the construction of pathological harmonic functions. This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions (potential theory), or an interest in holomorphic approximation.

    • Mathematics

Diamond, a Paradox Logic


Author: Nathaniel Hellerstein
Publisher: World Scientific
ISBN: 9810228503
Category: Mathematics
Page: 257
View: 8256
"This book should be interesting for everyone, and especially for logicians".Mathematical Reviews, 1999

    • Mathematics

Advanced Calculus

Revised
Author: Lynn Harold Loomis,Shlomo Sternberg
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category: Mathematics
Page: 596
View: 9949
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

    • Mathematics

Classical Invariant Theory


Author: Peter J. Olver
Publisher: Cambridge University Press
ISBN: 9780521558211
Category: Mathematics
Page: 280
View: 3575
The book is a self-contained introduction to the results and methods in classical invariant theory.