The LÃvy 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 LÃvyâLaplace 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 LÃvy Laplacian and the symmetrized LÃvy Laplacian as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with LÃvy Laplacians and to LÃvyâLaplace operators for example superconductivity theory the theory of control systems the Gauss random field theory and the YangâMills 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. Language: English