Functional analysis and differential equations in abstract spaces

Author(s)

• Zaidman, Samuel

Bibliographic Information

Functional analysis and differential equations in abstract spaces

Samuel Zaidman

（Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 100）

Chapman & Hall/CRC, c1999

Note

Includes bibliographical references (p. [208]-209) and indexes

Description and Table of Contents

Description

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.

Table of Contents

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 = f in Hilbert Space Solution of the Weak Neumann Problem in an Arbitrary Open Set of Rn References Subject Index Index of Symbols

by "Nielsen BookData"

Details

• NCID: BA42441006
• ISBN:
  • 1584880112
• LCCN: 98054425
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton, Fla.
• Pages/Volumes: 226 p.
• Size: 25 cm
• Classification:
  • LCC : QA320
  • DC21 : 515/.7
• Subject Headings:
  • LCSH : Functional analysis
  • LCSH : Differential equations
  • LCSH : Hilbert space
  • LCSH : Banach spaces
• Parent Bibliography ID:
  • BA41758925