Fourier analysis and semigroups
著者
書誌事項
Fourier analysis and semigroups
（Pseudo differential operators and Markov processes / Niels Jacob, v. 1）
Imperial College Press, c2001
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内容説明・目次
内容説明
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.
目次
- 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.
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