J. Aczel, J. Dhombres, Aczel J

Functional Equations in Several Variables

• Gebundenes Buch

Produktbeschreibung

Deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioral, and social sciences. The authors emphasize applications, although not at the expense of theory, and have kept the prerequisites to a minimum; the reader should be familiar with calculus and some simple structures of algebra and have a basic knowledge of Lebesque integration. For the applications the authors have included references and explained the results used. The book is designed so that the chapters may be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. Each chapter concludes with exercises and further results, 400 in all, which extend and test the material presented in the text. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography of over 1600 items. This volume will be of interest to professionals and graduate students in pure and applied mathematics.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 480
• Erscheinungstermin: 26. Februar 2004
• Englisch
• Abmessung: 240mm x 161mm x 30mm
• Gewicht: 881g
• ISBN-13: 9780521352765
• ISBN-10: 0521352762
• Artikelnr.: 21763922

Inhaltsangabe

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.