Functional Equations in Several Variables
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This treatise deals with modern theory of functional equations in several variables and their applications to mathematics. Booknews The title continues with applications to mathematics, information theory and to the natural and social sciences, and indeed: it is applications which have largely inspired the development of this wonderful field, in which clever trickery is the rule. Open the book at random, skim for a few paragraphs and you will arrive soon enough at a point where a non-mathematical research problem is posed and developed to the stage where it gives rise to a functional equation, whereupon methods of solution are discussed and their ramifications described. So it goes, for twenty absorbing chapters, most of which will be accessible to determined undergraduates. A final chapter sketches the rich history of the subject. The "selective bibliography" contains more than 1600 entries! Exercises (with hints) and further results appear at the end of each chapter. Attractively produced. An immensely valuable resource. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)
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, medialityand 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.
