Functional Analysis and Differential Equations in Abstract Spaces - Rilegato

Zaidman, S D

Rilegato

ISBN 10: 1584880112 ISBN 13: 9781584880110

Casa editrice: Chapman and Hall/CRC, 1999

Riassunto

Functional Analysis and Differential Equations in Abstract Spaces provides an elementary treatment of this very classical topic-but presented in a rather unique way. The author offers the functional analysis interconnected with specialized sections on differential equations, thus creating a self-contained text that includes most of the necessary functional analysis background, often with quite complete proofs. Beginning with some basic functional analysis-Hilbert and Banach spaces and their linear operators-Dr. Zaidman then presents some results about the abstract Cauchy problem, in implicit or explicit form, and related semigroups of operators, weak and ultraweak solutions, the uniqueness of the Cauchy problem, the uniqueness of bounded ultraweak solutions, and the well-posed ultraweak Cauchy problem. He goes on to present some results on almost-periodic solutions and an asymptotic result for a differential inequality in ultraweak form. Designed to inspire interest in this elegant and rapidly growing field of mathematics, this volume presents the material at a relatively elementary level-requiring a minimum of knowledge and ability in the field-yet with depth sufficient for understanding various special topics in operator differential equations. Many of the research results appear for the first time in book form and some for the first time anywhere. Researchers in the theories of differential equations in abstract spaces, semigroups of operators, and evolution equations, along with researchers in mathematical physics and quantum mechanics will find this work both enlightening and accessible.

Su questo libro

Contenuti

Introduction
Hilbert Space, Definitions, First Results
Banach Spaces and Linear Operators
Duality, the Hahn-Banach Extension Theorem
Some Singular (Implicit) Abstract Differential Equations
Semigroups of Class C0 and the Abstract Cauchy Problem
Compact Linear Operators
Continuous Symmetric Operators in Hilbert Spaces
Semidynamical Systems and C0-Semigroups
Uniqueness of Weak Solutions for a Second-Order Abstract Cauchy Problem in Hilbert Space
Uniqueness of Ultraweak Solutions for a First Order Abstract Cauchy Problem in Banach Space
Uniqueness of Bounded Ultraweak Solutions in Hilbert Space
Almost-Periodic Solutions I
The Well-Posed Ultraweak Cauchy Problem and Related Semigroups of Operators
Asymptotic Result for Ultraweak Differential Inequalities in Hilbert Space
Almost-Periodic Solutions II
Variational Form of the Equation Au = ƒ in Hilbert Space
Solution of the Weak Neumann Problem in an Arbitrary Open Set of Rn
References
Subject Index
Index of Symbols

Dettagli dell?edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 1584880112
• ISBN 13: 9781584880110
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 215
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile