Kategoria BISAC: Mathematics >> Functional Analysis

The notions of transfer function and characteristic functions proved to be fundamental in the last fifty years in operator theory and in system theory. Moshe Livsic played a central role in developing these notions, and the book contains a selection of carefully chosen refereed papers dedicated to his memory. Topics include classical operator theory, ergodic theory and stochastic processes, geometry of smooth mappings, mathematical physics, Schur analysis and system theory. The variety of topics attests well to the breadth of Moshe Livsic's mathematical vision and the deep impact of his...

This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the Fejer property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative schemes. Applications to parallelization, randomization and linear programming are also considered.

Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries. The author explains key ideas, difficult proofs, and important applications in a succinct, accessible, and unified manner.

The book first discusses Sobolev inequalities in various settings, including the Euclidean...

Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation. Key features and topics: Extensive usage...

Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces.

This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schroder s and Abel s functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and...