Spectral properties and a Parseval’s equality in the singular case for q-Dirac problem

Abstract

Abstract This paper is devoted to studying a q-analog of the singular Dirac problem. First, we investigate some spectral properties of the problem. Then we prove the existence of a spectral function and establish a Parseval’s equality, for the singular q-Dirac system in a Hilbert space. Although there were given some results for this type of problem, we think that Parseval’s equality has not been studied yet.

Keywords

• q-Dirac problem
• singularity
• spectral function
• Parseval’s equality