Functional Equations in Several Variables

This treatise deals with modern theory of functional equations in several variables and their applications to mathematics.

J. Aczel (Author), J. Dhombres (Author)

9780521352765, Cambridge University Press

Hardback, published 6 April 1989

480 pages
23.4 x 15.6 x 3.5 cm, 0.798 kg

"...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

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.

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, quasi-extensions 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 Pexider-type 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 self-distributivity
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.

Subject Areas: Functional analysis & transforms [PBKF]