Partial differential equations and operators Fundamental solutions and semigroups Part II
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740304572
Table of contents: title: Content; title: To see Section 1–4 download Partial differential equations and operators: Part I; title: The Author; title: Preface; title: 1. Distributions, differential operators and examples; title: 1.1. Introduction; title: 1.2. Topics to be treated in this book; title: 1.3. Partition of unity; title: 1.4. Test functions and distributions; title: 1.5. Tempered distributions and Fourier transforms; title: 1.6. Examples of Fourier transforms; title: 2. Fundamental solutions; title: 2.1. Introduction and examples; title: 3. Fundamental solutions of the wave operator; title: 3.1. Fundamental solutions of the wave operator in one space dimension; title: 3.2. Fundamental solutions of the wave equationin several space dimensions; title: 4. Proofs of some main results; title: 4.1. Convolution products: formulation of some results; title: 4.2. Fourier transform and its inverse; title: 4.3. Theorem of Malgrange and Ehrenpreis; title: 4.4. Sobolev theory; title: 4.5. Elliptic operators; title: 4.6. 1 Sobolev spaces; title: 4.7. Paley-Wiener theorems; title: 4.8. Multiplicative distributions; title: 5. Operators in Hilbert space Part; title: 5.1. Some results in Banach algebras; title: 5.2. Closed linear operators; title: 6. Operator semigroups and Markov processes; title: 6.1. Generalities on semigroups; title: 6.2. Examples; title: 6.3. Markov processes; title: 6.4. Feynman-Kac semigroups Part II; title: 6.5. Harmonic functions on a strip; title: 7. Elements of functional analysis; title: 7.1. Theorem of Hahn-Banach; title: 7.2. Banach-Steinhaus theorems: barreled spaces; title: 7.3. Subjects for further research and presentations; title: 7.4. Bibliography