Generalized classical and quantum signal theories on hypergroups. Part 2. Quantum signal theory

Abstract

In this work we develop two topics in sequence and show their inter-relation. The first concerns on general notions of the classical signal theory on Abelian hypergroups. The sec­ond concerns the quantum generalized harmonic analysis of quantum signals. The basic ob­jects of the quantum harmonic analysis based on quantum Fourier transforms (including quantum MPT) are related not to (=quantum signals) f and quantum spectra F associated with classical signals and spectra as follows: , where the Q is so-called the Weyl quantization procedure. We study classical and generalized quantum convolutions and correlations of quantum signals (Hermitean operators) and spectra  .