Operator Theory

Advances and Applications

By: Alexander Ya. Shklyar

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Hardcover | 18 February 1997

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236 Pages

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23.39 x 15.6 x 1.42

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Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood.

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Preface
Introduction
Joint spectrum of commuting normal operators and its position. Estimates for roots of second order polynomials. Definition of well-posedness of boundary-value problems
Well-posedness of boundary-value problems for equation (1) in the case of commuting self-adjoint A and B
The Cauchy problem
Boundary-value problems on a finite segment
Boundary behaviour of an integral transform R(t) as t [actual symbol not reproducible] 0 depending on the sub-integral measure
Initial data of solutions
The general form of weak solutions
Fatou-Riesz property
Extension of weak solutions
Stability and stabilization of weak solutions
The Dirichlet problem on a half-line
The Neumann problem on a half-line
Commentaries on the literature
Bibliography
Index
List of symbols
Table of Contents provided by Blackwell. All Rights Reserved.

Operator Theory

Advances and Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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