Pseudo Differential Operators and Markov Processes: Fourier Analysis and Semigroups, 1. kötetWorld Scientific, 2001 - 516 oldal After recalling essentials of analysis OCo including functional analysis, convexity, distribution theory and interpolation theory OCo 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. Sample Chapter(s). Introduction: Pseudo Differential Operators and Markov Processes (207 KB). Chapter 1: Introduction (190 KB). Contents: Essentials from Analysis: Calculus Results; Convexity; Some Interpolation Theory; Fourier Analysis and Convolution Semigroups: The PaleyOCoWienerOCoSchwartz Theorem; Bounded Borel Measures and Positive Definite Functions; Convolution Semigroups and Negative Definite Functions; The L(r)vyOCoKhinchin 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. Readership: Graduate students, researchers and lecturers in analysis & differential equations, stochastics, probability & statistics, and mathematical physics." |
Tartalomjegyzék
Introduction | 3 |
Essentials from Analysis | 11 |
75 | 31 |
98 | 38 |
120 | 46 |
9 | 172 |
One Parameter Semigroups | 253 |
383 | 417 |
451 | |
479 | |
Más kiadások - Összes megtekintése
Pseudo Differential Operators & Markov Processes: Fourier analysis ..., 1. kötet Niels Jacob Korlátozott előnézet - 2001 |
Gyakori szavak és kifejezések
analytic Banach space bilinear form Borel measure characterise closable CN(R compact sets continuous contraction semigroup continuous embeddings continuous negative definite converges convex convolution semigroup Corollary denote densely defined Dirichlet form Dirichlet operator Example exists extension Əxj Feller semigroup follows Fourier transform function f Further let hence Hilbert space holds implies integral Ju(x kernel L¹(R L²(R Laplace transform Lemma Let f Let Tt)to Lévy linear operator Lº(R LP(R mapping maximum principle measurable functions monotone functions Moreover negative definite function norm pointwise positive definite functions positive maximum principle positivity preserving Proposition prove pseudo-differential operators Pt(x R.L. Schilling representation Rn Rn satisfying the positive Section sequence strongly continuous contraction sub-Markovian semigroup subspace supp Suppose symmetric topological vector space topology µ(ds µ(dt µ(dx