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

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

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 th...

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Veröffentlicht in:Communications Series A1 Mathematics & Statistics 2023-03, Vol.72 (1), p.247-258
Hauptverfasser: SERTBAŞ, Meltem, SARAL, Coşkun
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description 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.
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title q$-Difference Operator on $L_q^{2}( 0, + \infty )
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