UID:
almafu_9959240274702883
Format:
1 online resource (xiii, 462 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88182-5
,
1-107-10263-4
,
1-107-08798-8
,
1-107-10009-7
,
1-107-09416-X
,
1-139-08657-X
Series Statement:
Encyclopaedia of mathematics and its applications ; v. 31
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Half Title; Title; Copyright; Dedication; PREFACE; FURTHER INFORMATION; 1 Axiomatic motivation of vector addition; Exercises and further results; 2 Cauchy's equation. Hamel basis; 2.1 General considerations, extensions, and regular solutions; 2.2 General solutions; Exercises and further results; 3 Three further Cauchy equations. An application to information theory; Exercises and further results; 4 Generalizations of Cauchy's equations to several muitiplace vector and matrix functions. An application to geometric objects; 4.1 Multiplace and vector functions
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4.2 A matrix functional equation and a characterization of densities in the theory of geometric objects4.3 Pexider equations; 4.4 Cauchy-type equations on semigroups; Exercises and further results; 5 Cauchy's equations for complex functions. Applications to harmonic analysis and to information measures; 5.1 Cauchy's equation and the exponential equation for complex functions; 5.2 Endomorphisms of the real and complex fields; 5.3 Bohr groups; 5.4 Recursive entropies; Exercises and further results
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6 Conditional Cauchy equations. An application to geometry and a characterization of the Heaviside functionExercises and further results; 7 Addundancy, extensions, quasi-extensions and extensions almost everywhere. Applications to harmonic analysis and to rational decision making; 7.1 Extensions and quasi-extensions; 7.2 Extensions almost everywhere and integral transforms; 7.3 Consensus allocations; Exercises and further results; 8 D' Alembert's functional equation. An application to noneuclidean mechanics; Exercises and further results
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9 Images of sets and functional equations. Applications to relativity theory and to additive functions bounded on particular sets9.1 Equations containing images of sets and chronogeometry; 9.2 Sets on which bounded additive functions are continuous; Exercises and further results; 10 Some applications of functional equations in functional analysis, in the geometry of Banach spaces and in valuation theory; 10.1 Functional equations and extreme points; 10.2 Totally monotonic functions and extreme rays; 10.3 A characterization of strictly convex normed spaces
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10.4 Isometries in real normed spaces10.5 A topology on the set of all solutions of a functional equation: the Bohr group; 10.6 Valuations on the fields of rational and of real numbers; Exercises and further results; 11 Characterizations of inner product spaces. An application to gas dynamics; 11.1 Quadratic functionals: a characterization of inner product space; 11.2 Triangles in normed spaces: a second characterization of inner product spaces; 11.3 Orthogonal additivity; 11.4 An application to gas dynamics; Exercises and further results
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12 Some related equations and systems of equations. Applications to cambinatorics and Markov processes
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English
Additional Edition:
ISBN 0-521-06389-2
Additional Edition:
ISBN 0-521-35276-2
Language:
English
