Overview

The L vy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well-developed in recent years and this book is the first systematic treatment of the L vy-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 L vy Laplacian and the symmetrized L vy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with L vy Laplacians and to L vy-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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9781281836670

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.,. the book has been carefully written to facilitate access to the material, and although it is compact, it is full of important results on the Levy Laplacian and its related topics investigated during the last forty years. In conclusion the reviewer would like to recommend the present book to graduate students and researchers in functional analysis, partial differential equations and probability theory. Mathematical Reviews

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