$q$-Difference Operator on $L_q^{2}( 0, + \infty )$

Abstract

In this research, the minimal and maximal operators defined by $q$- difference expression are given in the Hilbert space $L_q^{2}( 0, + \infty )$. The existence problem of a $q^{-1}$-normal extension for the minimal operator is mentioned. In addition, the sets of the minimal operator spectrum and the maximal operator spectrum are examined.

Keywords

• $q$- difference operator
• minimal operator
• maximal operator
• $q$-formally normal operator
• $q$-normal operator
• spectrum

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