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An introduction to infinite-dimensional analysis. (English) Zbl 1109.46001
Universitext. Berlin: Springer (ISBN 3-540-29020-6/pbk). x, 210 p. (2006).
This is an extended version of the author’s “An introduction to infinite-dimensional analysis” published by Scuola Normale Superiore, Pisa (2001; Zbl 1065.46001). In the paragraphs 1–8 there are only minor changes, the paragraphes 9–11 have completely been reworked. They cover now \(L^2\)-spaces with respect to Gaussian measures, Sobolev spaces for a Gaussian measure with sections on Wiener chaos, Dirichlet forms, PoincarĂ© and log-Sobolev inequalities as well as hypercontractivity. The final paragraph 11 is on gradient systems and treats more recent developments.
A well written textbook (even an introductory research monograph), suitable for teaching a graduate course.

MSC:
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
46G10 Vector-valued measures and integration
47D07 Markov semigroups and applications to diffusion processes
60J65 Brownian motion
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