{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T21:57:25Z","timestamp":1780523845540,"version":"3.54.1"},"reference-count":45,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T00:00:00Z","timestamp":1646870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we give another generalization of second order backward difference operator \u22072 by introducing its quantum analog \u2207q2. The operator \u2207q2 represents the third band infinite matrix. We construct its domains c0(\u2207q2) and c(\u2207q2) in the spaces c0 and c of null and convergent sequences, respectively, and establish that the domains c0(\u2207q2) and c(\u2207q2) are Banach spaces linearly isomorphic to c0 and c, respectively, and obtain their Schauder bases and \u03b1-, \u03b2- and \u03b3-duals. We devote the last section to determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the operator \u2207q2 over the Banach space c0 of null sequences.<\/jats:p>","DOI":"10.3390\/sym14030557","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T20:19:10Z","timestamp":1646943550000},"page":"557","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["The Spectrum of Second Order Quantum Difference Operator"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3435-8417","authenticated-orcid":false,"given":"Taja","family":"Yaying","sequence":"first","affiliation":[{"name":"Department of Mathematics, Dera Natung Government College, Itanagar 791113, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0644-0600","authenticated-orcid":false,"given":"Bipan","family":"Hazarika","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Gauhati University, Gauhati 781014, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Binod","family":"Chandra Tripathy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tripura University, Agartala 799022, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4128-0427","authenticated-orcid":false,"given":"Mohammad","family":"Mursaleen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40001, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kac, V., and Cheung, P. 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