This Research Note addresses several pivotal problems in spectral theo ry and nonlinear functional analysis in connection with the analysis o f the structure set of zeroes of a general class of nonlinear operator s. Appealing to a broad audience, it contains many important contribut ions to linear algebra, linear functional analysis, nonlinear function analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and system. The result s presented cover a thirty-year period and cut across a variety of mat hematical fields.

Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory.

The book presents generalized solutions to the Cauchy...