The Lévy Laplacian / M.N. Feller.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

The Lévy Laplacian -- Lévy-Laplace operators -- Symmetric Lévy-Laplace operator -- Harmonic functions of infinitely many variables -- Linear elliptic and parabolic equations with Lévy Laplacians -- Quasilinear and nonlinear elliptic equation with Lévy Laplacians -- Nonlinear parabolic equations with Lévy Laplacians.

The Lévy 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 Lévy-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 Lévy Laplacian and the symmetrized Lévy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with Lévy Laplacians and to Lévy-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.