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dc.contributor.authorPashaev, Oktay
dc.contributor.authorNalcı, Şengül
dc.date.accessioned2017-05-23T07:39:18Z
dc.date.available2017-05-23T07:39:18Z
dc.date.issued2014-01
dc.identifier.citationPashaev, O., and Nalcı, Ş. (2014). Q-analytic functions, fractals and generalized analytic functions. Journal of Physics A: Mathematical and Theoretical, 47(4). doi:10.1088/1751-8113/47/4/045204en_US
dc.identifier.issn1751-8113
dc.identifier.urihttps://doi.org/10.1088/1751-8113/47/4/045204
dc.identifier.urihttp://hdl.handle.net/11147/5573
dc.description.abstractWe introduce a new class of complex functions of complex argument which we call q-analytic functions. These functions satisfy q-Cauchy-Riemann equations and have real and imaginary parts as q-harmonic functions. We show that q-analytic functions are not the analytic functions. However some of these complex functions fall in the class of generalized analytic functions. As a main example we study the complex q-binomial functions and their integral representation as a solution of the D-bar problem. In terms of these functions the complex q-analytic fractal, satisfying the self-similar q-difference equation is derived. A new type of quantum states as q-analytic coherent states and corresponding q-analytic Fock-Bargmann representation are constructed. As an application, we solve quantum q-oscillator problem in this representation, and show that the wave functions of quantum states are given by complex q-binomials.en_US
dc.description.sponsorshipThe Scientific and Technological Research Council of Turkey (110T679); Izmir Institute of Technologyen_US
dc.language.isoengen_US
dc.publisherIOP Publishingen_US
dc.relationinfo:eu-repo/grantAgreement/TUBITAK/TBAG/110T679en_US
dc.relation.isversionof10.1088/1751-8113/47/4/045204en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectFock-Bargman representationen_US
dc.subjectFractalsen_US
dc.subjectGeneralized analytic functionsen_US
dc.subjectCalculusen_US
dc.subjectQuantumen_US
dc.titleQ-analytic functions, fractals and generalized analytic functionsen_US
dc.typearticleen_US
dc.contributor.authorIDTR57865en_US
dc.contributor.authorIDTR57807en_US
dc.contributor.iztechauthorPashaev, Oktay
dc.contributor.iztechauthorNalcı, Şengül
dc.relation.journalJournal of Physics A: Mathematical and Theoreticalen_US
dc.contributor.departmentİYTE, Fen Fakültesi, Matematik Bölümüen_US
dc.identifier.volume47en_US
dc.identifier.issue4en_US
dc.identifier.wosWOS:000329754200009
dc.identifier.scopusSCOPUS:2-s2.0-84892584645
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US


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