Real and complex analysis. (Reelle und komplexe Analysis. Übersetzt aus dem Englischen von Uwe Krieg.) (German) Zbl 0954.26001

München: Oldenbourg Verlag. xiv, 499 S. (1999).
There is a vast literature of textbooks on mathematical analysis, both real and complex. Walter Rudin is well-known as the author of one of the best textbooks on “Principles of mathematical analysis” (1953; Zbl 0052.05301, and many other editions) which now has been translated into 13 languages. The most recent edition of the book under review has appeared 3 years ago (1997) and has also found the worldwide distribution it deserves. It is really good news that now a German translation is available, too, at a reasonable price.
The book succeeds in bridging the somewhat artificial gap between real and complex analysis and covers surprisingly many important fields of advanced mathematical analysis, such as measure and integration, Hilbert and Banach spaces, Fourier transforms, harmonic functions and conformal mappings, Lebesgue and Hardy spaces, and approximation problems. A more detailed description of the contents may be found in the review of the Spanish translation (1985; Zbl 0613.26001). Without any doubt, this book may be enthusiastically recommended to every teacher and student, as well as to researchers in other fields of mathematics who have already given up looking for a good presentation of real and complex analysis as a whole.


26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable