Walter Rudin

von 4A: Dieses Lehrbuch geh rt mit seinem komprimierten, aber dennoch klaren Stil zu den Meisterwerken der mathematischen Lehrbuchliteratur. Der Verfasser behandelt mit methodisch-didaktischer Geschicklichkeit vollst ndig die Analysis einer und mehrerer Variablen. Dabei bietet Rudins "Analysis" viele Besonderheiten: So werden z. B. das Riemann-Stieltjes-Integral, die Lebesgue'sche Theorie, die Gamma-Funktion, Differentialformen oder der Satz von Stone-Weierstra sehr ausf hrlich besprochen. Damit zeichnet sich das Buch gegen ber anderen einf hrenden Analysisb chern aus. Die profunde Darstellung auf hohem Niveau richtet sich vor allem an fortgeschrittene Mathematiker. F r Studenten im Hauptfach Mathematik ist das Buch eine Bereicherung und ein wertvolles Nachschlagewerk.

Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory. Reprint of the Interscience Publishers, New York, 1962 edition.

""Fourier Analysis On Groups"" is a comprehensive mathematical text written by Walter Rudin, published as part of the Interscience Tracts in Pure and Applied Mathematics series. The book is aimed at graduate students and researchers in the field of mathematical analysis and covers the theory of Fourier analysis on locally compact groups. The text begins with an introduction to the basic concepts of group theory and harmonic analysis, before delving into the more advanced topics of Fourier transforms and Plancherel's theorem. Rudin also covers topics such as convolution, the Fourier-Stieltjes algebra, and the Fourier transform on non-abelian groups. Throughout the book, Rudin provides clear and concise explanations of the mathematical concepts, accompanied by numerous examples and exercises to aid the reader's understanding. The text is well-organized and easy to follow, making it a valuable resource for both students and researchers in the field of Fourier analysis on groups. Overall, ""Fourier Analysis On Groups"" is a highly regarded mathematical text that has been praised for its clarity, depth, and rigor. It is an essential reference for anyone interested in the theory of Fourier analysis on groups and its applications in mathematical analysis and related fields. Additional Editor Is J. J. Stoker. This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Function Theory in the Unit Ball of Cn. From the reviews: "…The book is easy on the reader. The prerequisites are minimal—just the standard graduate introduction to real analysis, complex analysis (one variable), and functional analysis. This presentation is unhurried and the author does most of the work. …certainly a valuable reference book, and (even though there are no exercises) could be used as a text in advanced courses." R. Rochberg in Bulletin of the London Mathematical Society. "…an excellent introduction to one of the most active research fields of complex analysis. …As the author emphasizes, the principal ideas can be presented clearly and explicitly in the ball, specific theorems can be quickly proved. …Mathematics lives in the book: main ideas of theorems and proofs, essential features of the subjects, lines of further developments, problems and conjectures are continually underlined. …Numerous examples throw light on the results as well as on the difficulties." C. Andreian Cazacu in Zentralblatt für Mathematik

..". Ein solches Werk mu man hintereinander weg von vorn bis hinten lesen, und das habe ich jetzt getan. Ich verstehe von der modernen Mathematik fast nichts. Rudin versteht es aber gro artig, sein Leben vor und nach dem Anschlu sterreichs an Hitler-Deutschland, exemplarisch f r viele andere, darzustellen. Er tut dies wohltuend sachlich und leidenschaftslos. Das ist f r ihn, der noch rechtzeitig entkommen ist, nat rlich leichter als f r jemanden, der durch die H lle gegangen ist und berlebt hat. Beeindruckend ist seine treffende Analyse der Charaktere des Durchschnitts- sterreichers, -Franzosen, -Engl nders, -Polen. Mit Deutschen hat er wenig Erfahrung gemacht, und das Wesen des Durchschnitts-Amerikaners objektiv zu analysieren ist f r ihn, der inzwischen f nf Jahrzehnte in den USA lebt und zum Amerikaner geworden ist, nat rlich nicht m glich. Rudin hat daher, korrekterweise, diese beiden Volkscharaktere nicht direkt beschrieben. Es ist schade, da eine ebenso n chterne Analyse des Wesens dieser beiden V lker fehlt. Ich habe das Buch mit gro em Genu gelesen ..." (Professor Friedrich Liebau) ..". Im zweiten Teil bietet Rudin eine Auswahl seiner Arbeiten ... Diese Themen liegen zwar au erhalb der Schulmathematik, sind aber leicht beschreibbar und in ihren Beweisen kurz und pr gnant." (PM - Praxis der Mathematik in der Schule, 01, Januar 2001)

In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.

This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

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.

Explains set theory, sequences, continuity, differentiation, integrals, and vector-space concepts