Functional equations on hypergroups
The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful con...
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| Hlavný autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
New Jersey
World Scientific Publishing Co. Pte. Ltd
2012
World Scientific World Scientific Publishing Company WORLD SCIENTIFIC |
| Vydanie: | 1 |
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| ISBN: | 9789814407007, 9814407003 |
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Obsah:
- Functional equations on hypergroups -- Preface -- Contents -- Chapter 1: Introduction -- Chapter 2: Polynomial hypergroups in one variable -- Chapter 3: Polynomial hypergroups in several variables -- Chapter 4: Sturm-Liouville hypergroups -- Chapter 5: Two-point support hypergroups -- Chapter 6: Spectral analysis and synthesis on polynomial hypergroups -- Chapter 7: Spectral analysis and synthesis on Sturm-Liouville hypergroups -- Chapter 8: Moment problems on hypergroups -- Chapter 9: Special functional equations on hypergroups -- Chapter 10: Difference equations on polynomial hypergroups -- Chapter 11: Stability problems on hypergroups -- Bibliography -- Index
- Intro -- Contents -- Preface -- 1. Introduction -- 1.1 Basic concepts and facts -- 1.2 Convolution of subsets -- 1.3 Invariant means on hypergroups -- 1.4 Haar measure on hypergroups -- 1.5 Exponential functions on hypergroups -- 1.6 Exponential families on hypergroups -- 1.7 Additive and multi-additive functions on hypergroups -- 1.8 Moment functions on hypergroups -- 1.9 Exponentials and additive functions on a special hypergroup -- 2. Polynomial hypergroups in one variable -- 2.1 Polynomial hypergroups in one variable -- 2.2 Exponential and additive functions on polynomial hypergroups -- 2.3 Moment functions on polynomial hypergroups -- 2.4 Moment functions on the SU(2)-hypergroup -- 3. Polynomial hypergroups in several variables -- 3.1 Polynomial hypergroups in several variables -- 3.2 Exponential and additive functions on multivariate polynomial hypergroups -- 3.3 Moment function sequences on multivariate polynomial hypergroups -- 4. Sturm-Liouville hypergroups -- 4.1 Sturm-Liouville functions -- 4.2 Exponentials and additive functions on Sturm-Liouville hypergroups -- 4.3 Moment functions on Sturm-Liouville hypergroups -- 5. Two-point support hypergroups -- 5.1 Conditional functional equations -- 5.2 Two-point support hypergroups of noncompact type -- 5.3 Moment functions on two-point support hypergroups of noncompact type -- 5.4 Two-point support hypergroups of compact type -- 5.5 The cosh hypergroup -- 5.6 Associated pairs of moment functions -- 6. Spectral analysis and synthesis on polynomial hypergroups -- 6.1 Spectral analysis and spectral synthesis on hypergroups -- 6.2 Basic concepts and facts -- 6.3 Spectral analysis on polynomial hypergroups in a single variable -- 6.4 Exponential polynomials on polynomial hypergroups in a single variable -- 6.5 Spectral synthesis on polynomial hypergroups in a single variable
- 6.6 Spectral analysis and spectral synthesis on multivariate polynomial hypergroups -- 6.7 Spectral analysis and moment functions -- 7. Spectral analysis and synthesis on Sturm-Liouville hypergroups -- 7.1 Exponential monomials on Sturm-Liouville hypergroups -- 7.2 Linear independence of special exponential monomials -- 7.3 Spectral analysis on Sturm-Liouville hypergroups -- 8. Moment problems on hypergroups -- 8.1 The moment problem in general -- 8.2 Uniqueness on polynomial hypergroups -- 8.3 The case of Sturm-Liouville hypergroups -- 8.4 An approximation result -- 9. Special functional equations on hypergroups -- 9.1 The sine functional equation on polynomial hypergroups -- 9.2 The cosine functional equation on polynomial hypergroups -- 9.3 The Levi-Civita functional equation -- 10. Difference equations on polynomial hypergroups -- 10.1 Introduction -- 10.2 Difference equations with 1-translation -- 10.3 Difference equations with general translation -- 11. Stability problems on hypergroups -- 11.1 Stability of exponential functions on hypergroups -- 11.2 Stability of additive functions on hypergroups -- 11.3 Superstability of a mixed-type functional equation -- 11.4 Superstability of generalized moment functions on hypergroups -- Bibliography -- Index