Functional equations in several variables ; with applications to mathematics, information theory and to the natural and social sciences
 Responsibility
 J. Aczél and J. Dhombres.
 Imprint
 Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1989.
 Physical description
 xiii, 462 p. : ill. ; 25 cm.
 Series
 Encyclopedia of mathematics and its applications v. 31
Online
Available online
At the library
Science Library (Li and Ma)
Stacks
Call number  Note  Status 

QA431 .A334 1989  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Aczél, J.
 Contributor
 Dhombres, Jean G.
Contents/Summary
 Bibliography
 Bibliography: p. [388]448.
 Contents

 Preface
 Further information
 1. Axiomatic motivation of vector addition
 2. Cauchy's equation: Hamel basis
 3. Three further Cauchy equations: an application to information theory
 4. Generalizations of Cauchy's equations to several multiplace vector and matrix functions: an application to geometric objects
 5. Cauchy's equations for complex functions: applications to harmonic analysis and to information measures
 6. Conditional Cauchy equations: an application to geometry and a characterization of the Heaviside functions
 7. Addundancy, extensions, quasiextensions and extensions almost everywhere: applications to harmonic analysis and to rational decision making
 8. D'Alembert's functional equation: an application to noneuclidean mechanics
 9. Images of sets and functional equations: applications to relativity theory and to additive functions bounded on particular sets
 10. Some applications of functional equations in functional analysis, in the geometry of Banach spaces and in valauation theory
 11. Characterizations of inner product spaces: an application to gas dynamics
 12. Some related equations and systems of equations: applications to combinatorics and Markov processes
 13. Equations for trigonometric and similar functions
 14. A class of equations generalizing d'Alembert and Cauchy Pexidertype equations
 15. A further generalization of Pexider's equation: a uniqueness theorem: an application to mean values
 16. More about conditional Cauchy equations: applications to additive number theoretical functions and to coding theory
 17. Mean values, mediality and selfdistributivity
 18. Generalized mediality: connection to webs and nomograms
 19. Further composite equations: an application to averaging theory
 20. Homogeneity and some generalizations: applications to economics
 21. Historical notes
 Notations and symbols
 Hints to selected 'exercises and further results'
 Bibliography
 Author index
 Subject index.
 (source: Nielsen Book Data)
 Publisher's summary

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 emphasize applications, though not at the expense of theory, so they have kept the prerequisites to a minimum; the reader need be 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 1989
 Series
 Encyclopedia of mathematics and its applications ; v.31
 Note
 Includes indexes.
 ISBN
 0521352762
 9780521352765