Functional Equations in Several Variables

By: J. Dhombres, J. Aczel

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Hardcover | 5 June 1989

At a Glance

Hardcover
480 Pages

Dimensions(cm)
16.6 x 24.2 x 3.0

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This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasise applications, though not at the expense of theory, so they have kept the prerequisites to a minimum; the reader should e familiar only with calculus and elementary algebra, and have a basic knowledge of Lebesgue integration. Where, for certain applications, more advanced topics are needed, the authors have included references and explained the results used. Moreover, the book has been designed so that the chapters can be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. At the end of each chapter are included exercises and further results, some 400 in all, which extend the material presented in the text and also test it. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography running to over 1600 items.

Industry Reviews

"The book has been designed so that the chapters can be read almost independently of each other. This beautifully written treatise is very useful as a reference book for research workers in the area." Mathematical Reviews "...this is an excellent reference book, in general, for senior and higher level physics students, and perhaps for numerical analysts working on computer algorithms...I would not hesitate to recommend this book to any physics and geophysics graduate students, as well as to some interested faculty members." Physics in Canada

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Preface
Further information
Axiomatic motivation of vector addition
Cauchy+s equation: Hamel basis
Three further Cauchy equations: an application to information theory
Generalizations of Cauchy+s equations to several multiplace vector and matrix functions: an application to geometric objects
Cauchy+s equations for complex functions: applications to harmonic analysis and to information measures
Conditional Cauchy equations: an application to geometry and a characterization of the Heaviside functions
Addundancy, extensions, quasi-extensions and extensions almost everywhere: applications to harmonic analysis and to rational decision making
D+Alembert+s functional equation: an application to noneuclidean mechanics
Images of sets and functional equations: applications to relativity theory and to additive functions bounded on particular sets
Some applications of functional equations in functional analysis, in the geometry of Banach spaces and in valauation theory
Characterizations of inner product spaces: an application to gas dynamics
Some related equations and systems of equations: applications to combinatorics and Markov processes
Equations for trigonometric and similar functions
A class of equations generalizing d+Alembert and Cauchy Pexider-type equations
A further generalization of Pexider+s equation: a uniqueness theorem: an application to mean values
More about conditional Cauchy equations: applications to additive number theoretical functions and to coding theory
Mean values, mediality and self-distributivity
Generalized mediality: connection to webs and nomograms
Further composite equations: an application to averaging theory
Homogeneity and some generalizations: applications to economics
Historical notes
Notations and symbols
Hints to selected +exercises and further results+
Bibliography
Author index
Subject index
Table of Contents provided by Publisher. All Rights Reserved.

Functional Equations in Several Variables

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