Kategoria BISAC: Mathematics >> Functional Analysis

This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials, making it accessible for those unfamiliar with graduate-level mathematics. Topics include topology, vector spaces, tensor spaces, Lebesgue integrals, and operators, to name a few. Two central issues the theory of Hilbert space and the operator theory and how they relate to quantum physics are covered extensively. Each chapter explains, concisely,...

This ambitious and substantial monograph, written by prominent experts in the field, presents the state of the art of convexity, with an emphasis on the interplay between convex analysis and potential theory; more particularly, between Choquet theory and the Dirichlet problem. The book is unique and self-contained, and it covers a wide range of applications which will appeal to many readers.

In recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such...

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.

This monograph is an introduction to some special aspects of topology, functional analysis, and analysis for the advanced reader. It also wants to develop a degree theory for function triples which unifies and extends most known degree theories. The book aims to be self-contained and many chapters could even serve as a basis of a course on the covered topics. Only knowledge in basic calculus and of linear algebra is assumed.