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 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.

Contents:

• Introduction
• Polynomial Hypergroups in One Variable
• Polynomial Hypergroups in Several Variables
• Sturm-Liouville Hypergroups
• Two-Point Support Hypergroups
• Spectral Analysis and Synthesis on Polynomial Hypergroups
• Spectral Analysis and Synthesis on Sturm-Liouville Hypergroups
• Moment Problems on Hypergroups
• Special Functional Equations on Hypergroups
• Difference Equations on Polynomial Hypergroups
• Stability Problems on Hypergroups

Readership: Researchers and post-graduate students working in hypergroups.
Key Features:

• The treatment applied here is completely new for those who are working in hypergroups: methods of functional equations and spectral synthesis have not been used before
• This treatment also enriches the theory of functional equations: no classical functional equational methods have been applied before on structures like hypergroups
• Several problems in both fields can be considered from a unique point of view of convolution type functional equations