| 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 |
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