Functional Differential Operators and Equations / Edition 1

Functional Differential Operators and Equations / Edition 1

by U.G. Kurbatov
     
 

ISBN-10: 0792356241

ISBN-13: 9780792356240

Pub. Date: 04/30/1999

Publisher: Springer Netherlands

The main topics are: the equivalence of the input-output stability of the equation x = and the invertibility of the operator in the class of casual operators; the equivalence of input-output and exponential sta bility; the equivalence of the dichotomy of solutions for the homogene ous equation x = 0 and the invertibility of the operator ; the propert ies of

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Overview

The main topics are: the equivalence of the input-output stability of the equation x = and the invertibility of the operator in the class of casual operators; the equivalence of input-output and exponential sta bility; the equivalence of the dichotomy of solutions for the homogene ous equation x = 0 and the invertibility of the operator ; the propert ies of Green's function; the independence of the stability of an equat ion from the norm on the space of solutions; shift invariant functiona l differential equations in Banach space; the possibility of the reduc tion of an equation of neutral type to an equation of retarded type; s pecial full subalgebras of integral and difference operators, and oper ators with unbounded memory; and the analogue of Fredholm's alternativ e for operators with almost periodic coefficients where one-sided inve rtibility implies two-sided invertibility.

Product Details

ISBN-13:
9780792356240
Publisher:
Springer Netherlands
Publication date:
04/30/1999
Series:
Mathematics and Its Applications (closed) Series, #473
Edition description:
1999
Pages:
434
Product dimensions:
1.00(w) x 6.14(h) x 9.21(d)

Table of Contents

Preface
Ch. IFunctional analysis preliminaries1
1.1Banach spaces and bounded linear operators1
1.2Diagrams7
1.3Lower norms14
1.4Banach algebras20
1.5Spaces of continuous and measurable functions31
1.6Infinite matrices44
1.7Tensor products61
1.8Conjugate spaces81
Ch. IIThe initial value problem97
2.1The causal invertibility98
2.2The causal spectrum106
2.3Spaces of smooth functions and distributions112
2.4The unique solubility127
2.5The evolutionary solubility136
2.6Criteria for evolutionary solubility140
Ch. IIIStability150
3.1Algebraic preliminaries150
3.2Input-output stability: discrete time157
3.3Input-output stability: continuous time162
3.4Exponential stability: discrete time171
3.5Exponential stability: continuous time179
3.6Exponential dichotomy: continuous time196
Ch. IVShift invariant operators and equations209
4.1Algebras of bounded measures209
4.2The Fourier transform221
4.3The Laplace transform239
4.4Convolution operators247
4.5Invertibility and causal invertibility267
Ch. VOperators with varying coefficients285
5.1Multiplication operators285
5.2Difference operators296
5.3Smoothing operators307
5.4Integral operators315
5.5Operators with locally fading memory322
5.6Operators with continuous coefficients333
Ch. VIDifferential difference equations343
6.1The local Fredholm property343
6.2The solubility for derivatives355
6.3The independence from the choice of a norm366
6.4Green's function372
6.5Almost periodic operators382
Comments403
Bibliography411
Index429
Notation Index433

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