In order to study discrete Abelian groups with wide range applications, the use of classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups is required. This book covers several different problems in this field and is unique in being the only comprehensive coverage of this topic. It should appeal to graduate students and researchers in harmonic analysis, spectral analysis, functional equations and hypergroups.
Author(s): Laszlo Szekelyhidi
Series: Springer Monographs in Mathematics
Edition: 1
Publisher: Springer
Year: 2006
Language: English
Pages: 119
1402046367......Page 1
Contents......Page 6
Preface......Page 8
1. Introduction......Page 15
2.1 The basic problems of spectral analysis and spectral synthesis......Page 20
2.2 Spectral analysis and synthesis on L[sup(1)](G)......Page 21
2.3 Spectral analysis and synthesis on L[sup(∞)](G)......Page 24
2.4 Spectral analysis and synthesis on C(G)......Page 30
3.1 Spectral analysis on discrete Abelian torsion groups......Page 37
3.3 Spectral analysis on commutative semigroups......Page 39
3.4 Spectral synthesis and polynomial ideals......Page 41
3.5 The failure of spectral synthesis on some types of discrete Abelian groups......Page 46
3.6 Spectral synthesis on Abelian torsion groups......Page 50
3.7 Polynomial functions and spectral synthesis......Page 54
4.1 Convolution type functional equations......Page 61
4.2 Mean value type functional equations......Page 64
4.3 A functional equation in digital filtering......Page 72
5.1 The Fourier transform of mean periodic functions......Page 80
5.2 The Fourier transform of exponential polynomials......Page 88
5.3 Applications to differential equations......Page 90
6.1 Spectral synthesis of difference equations......Page 93
6.2 Applications......Page 97
7.1 Polynomial hypergroups in one variable......Page 101
7.2 Spectral analysis on polynomial hypergroups in one variable......Page 106
7.3 Spectral synthesis on polynomial hypergroups in one variable......Page 108
8.1 Polynomial hypergroups in several variables......Page 112
8.2 Exponential and additive functions on multivariate polynomial hypergroups......Page 113
8.3 Spectral analysis and spectral synthesis on multivariate polynomial hypergroups......Page 116
References......Page 118
C......Page 122
E......Page 123
L......Page 124
S......Page 125
Z......Page 126
