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

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:72 Issue:1
$q$-Difference Operator on $L_q^{2}( 0, + \\infty )$

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

Authors : Meltem SERTBAŞ, Coşkun SARAL

Pages : 247-258

Doi:10.31801/cfsuasmas.1121701

View : 17 | Download : 11

Publication Date : 2023-03-30

Article Type : Research Paper

Abstract :In this research, the minimal and maximal operators defined by $q$- difference expression are given in the Hilbert space $L_q^{2}insert ignore into journalissuearticles values( 0, + \\infty );$. 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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