The L}}vy Laplacian [Hardcover]

This text was the first book on the L?vy Laplacian that generalized classical work and could be widely applied.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 2005 book was the first systematic treatment. With an extensive bibliography, the work will be valued by those working in functional analysis, partial differential equations and probability theory.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 2005 book was the first systematic treatment. With an extensive bibliography, the work will be valued by those working in functional analysis, partial differential equations and probability theory.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 was the first systematic treatment of the L?vyLaplace 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?vyLaplace operators, for example superconductivity theory, the theory of control systems, the Gauss random field theory, and the YangMills 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.Introduction; 1. The L?vy Laplacian; 2. L?vyLaplace operators; 3. Symmetric L?vyLaplace operators; 4. Harmonic functions of infinitely many variables; 5. Linear elliptic and parabolicls'