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

SERTBAŞ, MELTEM; SARAL, Coşkun

doi:10.31801/cfsuasmas.1121701

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

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, cilt.72, sa.1, ss.247-258, 2023 (ESCI)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 72 Sayı: 1
Basım Tarihi: 2023
Doi Numarası: 10.31801/cfsuasmas.1121701
Dergi Adı: Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
Sayfa Sayıları: ss.247-258
Anahtar Kelimeler: q-difference operator, minimal operator, maximal operator
Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.