A Panorama of Harmonic Analysis

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Author: Steven Krantz

Publisher: Cambridge University Press

ISBN: 9780883850312

Category: Mathematics

Page: 357

View: 334

A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.

Classical Fourier Analysis

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Author: Loukas Grafakos

Publisher: Springer

ISBN: 1493911945

Category: Mathematics

Page: 638

View: 9447

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.

Function Spaces and Partial Differential Equations

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Author: Ali Taheri

Publisher: Oxford University Press, USA

ISBN: 0198733135

Category: Differential equations, Partial

Page: 528

View: 1931

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Function Spaces and Partial Differential Equations

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Author: Ali Taheri

Publisher: Oxford University Press, USA

ISBN: 0198733151

Category: Differential equations, Partial

Page: 480

View: 7491

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Second Summer School in Analysis and Mathematical Physics

Topics in Analysis : Harmonic, Complex, Nonlinear, and Quantization : Second Summer School in Analysis and Mathematical Physics, Cuernavaca Morelos, Mexico, June 12-22, 2000

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Author: m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics

Publisher: American Mathematical Soc.

ISBN: 0821827081

Category: Mathematics

Page: 272

View: 8055

For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current research topics, particularly in analysis. The lectures are given by internationally recognized specialists in the fields. The topics covered in this Second Summer School include harmonic analysis, complex analysis, pseudodifferential operators, the mathematics of quantum chaos, and non-linear analysis.

A Tour Through Mathematical Logic

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Author: Robert S. Wolf

Publisher: MAA

ISBN: 9780883850367

Category: Mathematics

Page: 397

View: 6569

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

Classical and Modern Fourier Analysis

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Author: Loukas Grafakos

Publisher: Prentice Hall

ISBN: N.A

Category: Mathematics

Page: 931

View: 9345

For graduate-level courses in Fourier or harmonic analysis. Designed specifically for students (rather than researchers), this introduction to Fourier Analysis starts where the real and complex first-year graduate classes end.

Contemporary Authors

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Author: Gale Group,Terrie M. Rooney

Publisher: Gale Cengage

ISBN: 9780787620028

Category: Biography & Autobiography

Page: 500

View: 4254

Since 1962, Contemporary Authors has been an authoritative and comprehensive source of bibliographic and biographical information on important authors of the 20th century. This reference allows the user to access entries by author name, title of work or specific personal data.

Books in Print

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 6430

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Analysis II

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Author: Wolfgang Walter

Publisher: Springer-Verlag

ISBN: 3642967922

Category: Mathematics

Page: 398

View: 6368

Dem erfolgreichen Konzept von Analysis I folgend, wird auch im zweiten Teil dieses zweibändigen Analysis-Werkes viel Wert auf historische Zusammenhänge, Ausblicke und die Entwicklung der Analysis gelegt. Zu den Besonderheiten, die über den kanonischen Stoff des zweiten und dritten Semesters einer Analysisvorlesung hinausgehen, gehört das Lemma von Marston Morse. Die Grundtatsachen über die verschiedenen Integralbegriffe werden allesamt aus Sätzen über verallgemeinerte Limites (Moore-Smith-Konvergenz) abgeleitet. Die C?-Approximation von Funktionen (Friedrich Mollifiers) wird ebenso behandelt, wie die Theorie der absolut stetigen Funktionen. Bei den Fourierreihen wird die klassische Theorie in Weiterführung einer von Chernoff und Redheffer entwickelten Methode behandelt. Zahlreiche Beispiele, Übungsaufgaben und Anwendungen, z.B. aus der Physik und Astronomie runden dieses Lehrbuch ab.

Angewandte Mathematik: Body and Soul

Band 2: Integrale und Geometrie in IRn

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Author: Kenneth Eriksson,Donald Estep,Claes Johnson

Publisher: Springer-Verlag

ISBN: 3540269509

Category: Mathematics

Page: 362

View: 5742

"Angewandte Mathematik: Body & Soul" ist ein neuer Grundkurs in der Mathematikausbildung für Studienanfänger in den Naturwissenschaften, der Technik, und der Mathematik, der an der Chalmers Tekniska Högskola in Göteborg entwickelt wurde. Er besteht aus drei Bänden sowie Computer-Software. Das Projekt ist begründet in der Computerrevolution, die ihrerseits völlig neue Möglichkeiten des wissenschaftlichen Rechnens in der Mathematik, den Naturwissenschaften und im Ingenieurwesen eröffnet hat. Es besteht aus einer Synthese der mathematischen Analysis (Soul) mit der numerischen Berechnung (Body) sowie den Anwendungen. Die Bände I-III geben eine moderne Version der Analysis und der linearen Algebra wieder, einschließlich konstruktiver numerischer Techniken und Anwendungen, zugeschnitten auf Anfängerprogramme im Maschinenbau und den Naturwissenschaften. Weitere Bände behandeln Themen wie z.B. dynamische Systeme, Strömungsdynamik, Festkörpermechanik und Elektromagnetismus. Dieser Band entwickelt das Riemann-Integral, um eine Funktion zu einer gegebenen Ableitung zu bestimmen. Darauf aufbauend werden Differentialgleichungen und Anfangswertprobleme mit einer Vielzahl anschaulicher Anwendungen behandelt. Die lineare Algebra wird auf n-dimensionale Räume verallgemeinert, wobei wiederum dem praktischen Umgang und numerischen Lösungstechniken besonderer Platz eingeräumt wird. Die Autoren sind führende Experten im Gebiet des wissenschaftlichen Rechnens und haben schon mehrere erfolgreiche Bücher geschrieben. "[......] Oh, by the way, I suggest immediate purchase of all three volumes!" The Mathematical Association of America Online, 7.7.04

Grundbegriffe der Wahrscheinlichkeitsrechnung

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Author: A. Kolomogoroff

Publisher: Springer-Verlag

ISBN: 3642498884

Category: Mathematics

Page: 62

View: 9811

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Einführung in die Zahlentheorie

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Author: Peter Bundschuh

Publisher: N.A

ISBN: 9783540551782

Category: Number theory

Page: 334

View: 7822

Aus den Besprechungen: "Die vorliegende, umfangreiche Einf hrung ber cksichtigt st rker als andere die historische Entwicklung. Das bedeutet nicht, da der Autor grunds tzlich die ersten in der Literatur vorliegenden Beweise gew hlt hat, sondern da er angibt, wer die entsprechenden S tze gefunden hat und wie sie im Laufe der Zeit versch rft und verallgemeinert wurden. Das ist eines der Unterscheidungsmerkmale von anderen Einf hrungen in die Zahlentheorie. Ein zweites liegt in der Betonung der Theorie der Diophantischen Approximation, genauer in den Untersuchungen ber Irrationalit t und Transzendenz. Man findet zu diesem Thema auch als Kenner berraschende Schl sse. (...) Die Darstellung ist ausf hrlich, sehr gut lesbar und kommt ohne spezielle Kenntnisse aus. Das Buch kann daher jedem Studenten schon im nullten Semester empfohlen werden." #Monatshefte f r Mathematik#1