Functional equations in several variables: with applications to mathematics, information theory, and to the natural and social sciences

Abstract

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.