{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,4]],"date-time":"2023-04-04T09:13:17Z","timestamp":1680599597532},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> In this paper we start with a new detailed construction of the one-mode type q-L\u00e9vy-Meixner Fock space [Formula: see text] which serves to obtain the quantum decomposition associated with the q-deformed L\u00e9vy-Meixner white noise processes. More precisely, based on the notion of quantum decomposition and the orthogonalization of polynomials of noncommutative q-L\u00e9vy-Meixner white noise [Formula: see text], we study the chaos property of the noncommutative L<jats:sup>2<\/jats:sup>-space with respect to the vacuum expectation \u03c4. Next, we determine the distribution of the q-L\u00e9vy-Meixner operator J(\u03c7D) = \u27e8\u03c9, \u03c7D\u27e9 and as a consequence we give some useful properties of the q-L\u00e9vy-Meixner white noise process. <\/jats:p>","DOI":"10.1142\/s1230161220500110","type":"journal-article","created":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T11:05:42Z","timestamp":1598871942000},"page":"2050011","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Decomposition Associated with the <i>q<\/i>-Deformed L\u00e9vy\u2013Meixner White Noise"],"prefix":"10.1142","volume":"27","author":[{"given":"Anis","family":"Riahi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O.Box 66, Al-Majmaah 11952, Saudi Arabia"},{"name":"Department of Mathematics, Nabeul Preparatory Institute for Engineering Studies, Carthage University, Nabeul, Tunisia"}]},{"given":"Amine","family":"Ettaieb","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Higher School of Sciences and Technologies of Hammam-Sousse, MaPSFA laboratory, Sousse University, 4011, Hammam Sousse, Tunisia"}]}],"member":"219","published-online":{"date-parts":[[2020,8,28]]},"reference":[{"key":"p_2","first-page":"583","volume":"8","author":"Asai N.","year":"2004","journal-title":"Mathematics"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025798000363"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025710004103"},{"key":"p_6","first-page":"0012","volume":"16","author":"Accardi L.","year":"2013","journal-title":"Inf. Dim. Anal. Quant. Prob. Rel. Top."},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050084"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02100275"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-005-9000-7"},{"key":"p_15","first-page":"201","volume":"24","author":"Yuang Z. H.","year":"2008","journal-title":"English Series"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.7494\/OpMath.2018.38.5.699"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025703001444"},{"key":"p_20","first-page":"135","volume":"17","author":"Riahi A.","year":"2018","journal-title":"Operator Theory"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1016\/j.indag.2017.07.008"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161220500110","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T11:05:51Z","timestamp":1598871951000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1230161220500110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6]]},"references-count":12,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["10.1142\/S1230161220500110"],"URL":"https:\/\/doi.org\/10.1142\/s1230161220500110","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6]]}}}