Linear Functional Equations. Operator Approach: Operator Theory Advances and Applications: 83 - Softcover

Antonevich, Anatolij

Softcover

ISBN 10: 3034898517 ISBN 13: 9783034898515

Verlag: Birkhäuser, 2011

Über diesen Titel

Reseña del editor

In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa­ tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ­ ual representatives are related with problems arising in various areas of mathemat­ ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au­ tomorphisms of Banach algebras, and other problems.

Reseña del editor

This monograph presents a unified approach to the investi- gation of a general class of functional equations based on the examination of functional operators and Banach algebras generated by them, synthesizing methods involving dyna- mical systems, operator algebras and pseudodifferential operators. Special attention is paid to spectral properties of functional operators, and index formulas are derived. Applications are given to functional equations, boundary value problems and equations of convolution type. The book is addressed to a broad range of mathematicians and advanced students interested in functional analysis, differen- tial and integral equations.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2011
• ISBN 10: 3034898517
• ISBN 13: 9783034898515
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 196