Book contents
- Frontmatter
- Contents
- Dedication
- 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 valuation 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
5 - Cauchy's equations for complex functions. Applications to harmonic analysis and to information measures
Published online by Cambridge University Press: 05 November 2011
Book contents
- Frontmatter
- Contents
- Dedication
- 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 valuation 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
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- Functional Equations in Several Variables , pp. 52 - 72Publisher: Cambridge University PressPrint publication year: 1989