FUNCTIONAL EQUATIONS ON HYPERGROUPS

By: SZEKELYHIDI LASZLO

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Hardcover | 19 September 2012

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210 Pages

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22.86 x 15.24 x 1.27

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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 consequences of this delicate "marriage" where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods - and, sometimes, a new world of unexpected difficulties.

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Preface	p. vii
Introduction	p. 1
Basic concepts and facts	p. 1
Convolution of subsets	p. 6
Invariant means on hypergroups	p. 7
Haar measure on hypergroups	p. 11
Exponential functions on hypergroups	p. 20
Exponential families on hypergroups	p. 22
Additive and multi-additive functions on hypergroups	p. 23
Moment functions on hypergroups	p. 26
Exponentials and additive functions on a special hypergroup	p. 33
Polynomial hypergroups in one variable	p. 37
Polynomial hypergroups in one variable	p. 37
Exponential and additive functions on polynomial hypergroups	p. 39
Moment functions on polynomial hypergroups	p. 43
Moment functions on the SU(2)-hypergroup	p. 48
Polynomial hypergroups in several variables	p. 51
Polynomial hypergroups in several variables	p. 51
Exponential and additive functions on multivariate polynomial hypergroups	p. 52
Moment function sequences on multivariate polynomial hypergroups	p. 55
Sturm-Liouville hypergroups	p. 59
Sturm-Liouville functions	p. 59
Exponentials and additive functions on Sturm-Liouville hypergroups	p. 62
Moment functions on Sturm-Liouville hypergroups	p. 65
Two-point support hypergroups	p. 73
Conditional functional equations	p. 73
Two-point support hypergroups of noncompact type	p. 77
Moment functions on two-point support hypergroups of noncompact type	p. 78
Two-point support hypergroups of compact type	p. 86
The cosh hypergroup	p. 87
Associated pairs of moment functions	p. 88
Spectral analysis and synthesis on polynomial hypergroups	p. 95
Spectral analysis and spectral synthesis on hypergroups	p. 95
Basic concepts and facts	p. 96
Spectral analysis on polynomial hypergroups in a single variable	p. 99
Exponential polynomials on polynomial hypergroups in a single variable	p. 100
Spectral synthesis on polynomial hypergroups in a single variable	p. 103
Spectral analysis and spectral synthesis on multivariate polynomial hypergroups	p. 103
Spectral analysis and moment functions	p. 106
Spectral analysis and synthesis on Sturm-Liouville hypergroups	p. 109
Exponential monomials on Sturm-Liouville hypergroups	p. 109
Linear independence of special exponential monomials	p. 110
Spectral analysis on Sturm-Liouville hypergroups	p. 119
Moment problems on hypergroups	p. 123
The moment problem in general	p. 123
Uniqueness on polynomial hypergroups	p. 124
The case of Sturm-Liouville hypergroups	p. 128
An approximation result	p. 131
Special functional equations on hypergroups	p. 133
The sine functional equation on polynomial hypergroups	p. 133
The cosine functional equation on polynomial hypergroups	p. 138
The Lévi-Civitá functional equation	p. 142
Difference equations on polynomial hypergroups	p. 149
Introduction	p. 149
Difference equations with 1-translation	p. 150
Difference equations with general translation	p. 153
Stability problems on hypergroups	p. 161
Stability of exponential functions on hypergroups	p. 161
Stability of additive functions on hypergroups	p. 163
Superstability of a mixed-type functional equation	p. 165
Superstability of generalized moment functions on hypergroups	p. 168
Bibliography	p. 173
Index	p. 187
Table of Contents provided by Ingram. All Rights Reserved.

FUNCTIONAL EQUATIONS ON HYPERGROUPS

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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