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Functional Differential Operators and Equations : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - U. G. Kurbatov

Functional Differential Operators and Equations


Hardcover Published: 30th April 1999
ISBN: 9780792356240
Number Of Pages: 434

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This book deals with linear functional differential equations and operator theory methods for their investigation. The main topics are: the equivalence of the input-output stability of the equation "L"x = &mathsf; and the invertibility of the operator "L" in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation "L"x = 0 and the invertibility of the operator "L"; the properties of Green's function; the independence of the stability of an equation from the norm on the space of solutions; shift invariant functional differential equations in Banach space; the possibility of the reduction of an equation of neutral type to an equation of retarded type; special full subalgebras of integral and difference operators, and operators with unbounded memory; and the analogue of Fredholm's alternative for operators with almost periodic coefficients where one-sided invertibility implies two-sided invertibility. Audience: This monograph will be of interest to students and researchers working in functional differential equations and operator theory and is recommended for graduate level courses.

U.G. Kurbatov

Functional Differential Operators and Equations

"This book provides a thorough and rigorous presentation of the use of operator theory methods to study the linear theory of functional-differential equations . . . It is a practically self-contained book by means of which students and researchers working in functional analysis can be introduced to the abstract linear theory of functional-differential equations."-MATHEMATICAL REVIEWS

Functional analysis preliminariesp. 1
Banach spaces and bounded linear operatorsp. 1
Diagramsp. 7
Lower normsp. 14
Banach algebrasp. 20
Spaces of continuous and measurable functionsp. 31
Infinite matricesp. 44
Tensor productsp. 61
Conjugate spacesp. 81
The initial value problemp. 97
The causal invertibilityp. 98
The causal spectrump. 106
Spaces of smooth functions and distributionsp. 112
The unique solubilityp. 127
The evolutionary solubilityp. 136
Criteria for evolutionary solubilityp. 140
Stabilityp. 150
Algebraic preliminariesp. 150
Input-output stability: discrete timep. 157
Input-output stability: continuous timep. 162
Exponential stability: discrete timep. 171
Exponential stability: continuous timep. 179
Exponential dichotomy: continuous timep. 196
Shift invariant operators and equationsp. 209
Algebras of bounded measuresp. 209
The Fourier transformp. 221
The Laplace transformp. 239
Convolution operatorsp. 247
Invertibility and causal invertibilityp. 267
Operators with varying coefficientsp. 285
Multiplication operatorsp. 285
Difference operatorsp. 296
Smoothing operatorsp. 307
Integral operatorsp. 315
Operators with locally fading memoryp. 322
Operators with continuous coefficientsp. 333
Differential difference equationsp. 343
The local Fredholm propertyp. 343
The solubility for derivativesp. 355
The independence from the choice of a normp. 366
Green's functionp. 372
Almost periodic operatorsp. 382
Commentsp. 403
Bibliographyp. 411
Indexp. 429
Notation Indexp. 433
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792356240
ISBN-10: 0792356241
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 434
Published: 30th April 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.88  x 2.54
Weight (kg): 0.86