The Lévy Laplacian
著者
書誌事項
The Lévy Laplacian
（Cambridge tracts in mathematics, 166）
Cambridge University Press, 2005
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注記
Includes bibliographical references (p. 144-151) and index
内容説明・目次
内容説明
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.
目次
- Introduction
- 1. The Levy Laplacian
- 2. Levy-Laplace operators
- 3. Symmetric Levy-Laplace operators
- 4. Harmonic functions of infinitely many variables
- 5. Linear elliptic and parabolic equations with Levy Laplacians
- 6. Quasilinear and nonlinear elliptic equation with Levy Laplacians
- 7. Nonlinear parabolic equations with Levy Laplacians
- 8. Appendix. Levy-Dirichlet forms and associated Markov processes
- Bibliography
- Index.
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