Pseudo Differential Operators And Markov Processes, Volume I: Fourier Analysis And Semigroups

Niels Jacob (Autor)

Buch | Hardcover

516 Seiten

2001
Imperial College Press (Verlag)
9781860942938 (ISBN)

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This work covers 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.

After 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.

Essentials 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.