Description
Book SynopsisAfter recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students.
Trade Review"The book is carefully written and each chapter is concluded with interesting historical, contemporary, and bibliographical comments with indications for further reading." Mathematical Reviews, 2003
Table of ContentsEssentials from analysis: calculus results; convexity; some interpolation theory. Fourier analysis and convolution semigroups: the Paley-Wiener-Schwartz theorem; bounded Borel measures and positive definite functions; convolution semigroups and negative definite functions; the Levy-Khinchin formula for continuous negative definite functions; Bernstein functions and subordination of convolution semigroups; Fourier multiplier theorems. One parameter semigroups: strongly continuous operator semigroups; subordination in the sense of Bochner for operator semigroups; generators of Feller semigroups; Dirichlet forms and generators of sub-Markovian semigroups; and other papers.
