The Lévy Laplacian

ISBN-13: 9780521846226 / Angielski / Twarda / 2005 / 160 str.

M. N. Feller

Opis

The Levy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well developed in recent years and this book was the first systematic treatment of the Levy Laplace operator. The book describes the infinite-dimensional analogues of finite-dimensional results, and more especially those features which appear only in the generalized context. It develops a theory of operators generated by the Levy Laplacian and the symmetrized Levy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with Levy Laplacians and to Levy Laplace operators, for example superconductivity theory, the theory of control systems, the Gauss random field theory, and the Yang Mills equation. The book is complemented by an exhaustive bibliography. The result is a work that will be valued by those working in functional analysis, partial differential equations and probability theory."

Recenzje

Review of the hardback: '... a nicely written book ...' Zentralblatt MATH

Spis treści

Introduction; 1. The Lévy Laplacian; 2. Lévy–Laplace operators; 3. Symmetric Lévy–Laplace operators; 4. Harmonic functions of infinitely many variables; 5. Linear elliptic and parabolic equations with Lévy Laplacians; 6. Quasilinear and nonlinear elliptic equation with Lévy Laplacians; 7. Nonlinear parabolic equations with Lévy Laplacians; 8. Appendix. Lévy–Dirichlet forms and associated Markov processes; Bibliography; Index.