M. N. Feller

Levy Laplacian (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 24. November 2005
• Englisch
• ISBN-13: 9780511131448
• Artikelnr.: 38213917

Inhaltsangabe

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.

Rezensionen

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