Mathematics and Its Applications

By: U.G. Kurbatov

Write A Review

Hardcover | 30 April 1999

At a Glance

Hardcover
456 Pages

Dimensions(cm)
23.5 x 15.88 x 2.54

Hardcover

$379.01

or 4 interest-free payments of $94.75 with

Ships in 5 to 7 business days

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 Lx = &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 Lx = 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.

Industry Reviews

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

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Algebra Differential Calculus & Equations Integral Calculus & Equations

Preface
Functional analysis preliminaries	p. 1
Banach spaces and bounded linear operators	p. 1
Diagrams	p. 7
Lower norms	p. 14
Banach algebras	p. 20
Spaces of continuous and measurable functions	p. 31
Infinite matrices	p. 44
Tensor products	p. 61
Conjugate spaces	p. 81
The initial value problem	p. 97
The causal invertibility	p. 98
The causal spectrum	p. 106
Spaces of smooth functions and distributions	p. 112
The unique solubility	p. 127
The evolutionary solubility	p. 136
Criteria for evolutionary solubility	p. 140
Stability	p. 150
Algebraic preliminaries	p. 150
Input-output stability: discrete time	p. 157
Input-output stability: continuous time	p. 162
Exponential stability: discrete time	p. 171
Exponential stability: continuous time	p. 179
Exponential dichotomy: continuous time	p. 196
Shift invariant operators and equations	p. 209
Algebras of bounded measures	p. 209
The Fourier transform	p. 221
The Laplace transform	p. 239
Convolution operators	p. 247
Invertibility and causal invertibility	p. 267
Operators with varying coefficients	p. 285
Multiplication operators	p. 285
Difference operators	p. 296
Smoothing operators	p. 307
Integral operators	p. 315
Operators with locally fading memory	p. 322
Operators with continuous coefficients	p. 333
Differential difference equations	p. 343
The local Fredholm property	p. 343
The solubility for derivatives	p. 355
The independence from the choice of a norm	p. 366
Green's function	p. 372
Almost periodic operators	p. 382
Comments	p. 403
Bibliography	p. 411
Index	p. 429
Notation Index	p. 433
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Its Applications

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Integral Calculus & Equations

Backward Stochastic Volterra Integral Equations

Probability Theory and Stochastic Modelling

Multivariable Calculus Set Free

Infinitesimals Ride Again

Multivariable Calculus Set Free

Infinitesimals Ride Again

An Illustrative Guide to Multivariable and Vector Calculus

Theoretical and Computational Contact Micromechanics

Solid Mechanics and Its Applications

The Mittag-Leffler and Gamma Function

Oxford Mathematical Monographs

Choquet Integral and Monotone Sublinear Operators

Frontiers in Mathematics

Nonlinear Complex Systems II

Attractors, Solitons, and Waves

Convergence in Measure and in Category

Lecture Notes in Mathematics

Advanced Topics on Caputo Tempered Fractional Di?erential Equations with Applications

Measure and Integration

An Introductory Path Toward Functional Analysis and Probability

Lebesgue's Theory of Singular Integrals

Foundations of Modern Harmonic Analysis

A Problem-Solving Approach to Multi-Variable Calculus

Volume I

Tbilisi Analysis and PDE Seminar

Extended Abstracts of the 2024 Seminar Talks

Periodic Elliptic Partial Differential Operators

The Main Structures

From Classical Analysis to Analysis on Fractals

A Tribute to Robert Strichartz, Volume 2

Symmetry Analysis of Differential Equations

An Introduction

Mathematical Epidemiology and Fractional Calculus Applications

Industrial and Applied Mathematics

Integral Equations of the First Kind

Series on Soviet and East European Mathematics

Why Don't Rabbits Rule The World?

Mathematical answers to life's key questions

Integral Equations and Boundary Value Problems : Proceedings of the International Conference

Proceedings of the International Conference

Lectures on Ergodic Theory

Dover Books on Mathematics

Boundary Value Problems For Analytic Functions

SERIES IN PURE MATHEMATICS

The Computational Complexity of Differential and Integral Equations

An Information-Based Approach

This product is categorised by