INTRODUCTION TO GENERALIZED CLASSICAL AND QUANTUM SIGNAL AND SYSTEM THEORIES ON GROUPS AND HYPERGROUPS

摘要

In this paper we develop two topics in parallel and show their inter-and crossrelation. The first centers on general notions of the classical signal/system theory on finite Abelian hypergroups. The second concerns the quantum hyperharmonic analysis of quantum signals (Her-mitean operators associated with classical signals). We study classical and quantum generalized convolution hypergroup algebras of classical and quantum signals.