By J. Aczel
By J. Dhombres
Publisher: Cambridge University Press
Print Publication Year:1989
Online Publication Date:November 2011
Online ISBN:9781139086578
Hardback ISBN:9780521352765
Paperback ISBN:9780521063890
Book DOI: http://dx.doi.org/10.1017/CBO9781139086578
Subjects: Abstract analysis
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.
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pp. i-iv
pp. v-vii
pp. viii-viii
pp. ix-xiii
pp. xiv-xiv
1 - Axiomatic motivation of vector addition: Read PDF
pp. 1-10
2 - Cauchy's equation. Hamel basis: Read PDF
pp. 11-24
3 - Three further Cauchy equations. An application to information theory: Read PDF
pp. 25-33
4 - Generalizations of Cauchy's equations to several multiplace vector and matrix functions. An application to geometric objects: Read PDF
pp. 34-51
5 - Cauchy's equations for complex functions. Applications to harmonic analysis and to information measures: Read PDF
pp. 52-72
6 - Conditional Cauchy equations. An application to geometry and a characterization of the Heaviside functions: Read PDF
pp. 73-83
7 - Addundancy, extensions, quasi-extensions and extensions almost everywhere. Applications to harmonic analysis and to rational decision making: Read PDF
pp. 84-102
8 - D'Alembert's functional equation. An application to noneuclidean mechanics: Read PDF
pp. 103-113
9 - Images of sets and functional equations. Applications to relativity theory and to additive functions bounded on particular sets: Read PDF
pp. 114-128
10 - Some applications of functional equations in functional analysis, in the geometry of Banach spaces and in valuation theory: Read PDF
pp. 129-164
11 - Characterizations of inner product spaces. An application to gas dynamics: Read PDF
pp. 165-200
12 - Some related equations and systems of equations. Applications to combinatorics and Markov processes: Read PDF
pp. 201-208
13 - Equations for trigonometric and similar functions: Read PDF
pp. 209-227
14 - A class of equations generalizing d'Alembert and Cauchy Pexider-type equations: Read PDF
pp. 228-239
15 - A further generalization of Pexider's equation. A uniqueness theorem. An application to mean values: Read PDF
pp. 240-253
16 - More about conditional Cauchy equations. Applications to additive number theoretical functions and to coding theory: Read PDF
pp. 254-286
17 - Mean values, mediality and self-distributivity: Read PDF
pp. 287-297
18 - Generalized mediality. Connection to webs and nomograms: Read PDF
pp. 298-308
19 - Further composite equations. An application to averaging theory: Read PDF
pp. 309-344
20 - Homogeneity and some generalizations. Applications to economics: Read PDF
pp. 345-354
21 - Historical notes: Read PDF
pp. 355-378
Notations and symbols: Read PDF
pp. 379-381
Hints to selected ‘exercises and further results’: Read PDF
pp. 382-387
pp. 388-448
pp. 449-457
pp. 458-462
No references available.