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Title: Q-analytic functions, fractals and generalized analytic functions
Authors: Pashaev, Oktay
Nalcı, Şengül
Keywords: Fock-Bargman representation
Generalized analytic functions
Issue Date: Jan-2014
Publisher: IOP Publishing Ltd.
Source: Pashaev, O., and Nalcı, Ş. (2014). Q-analytic functions, fractals and generalized analytic functions. Journal of Physics A: Mathematical and Theoretical, 47(4). doi:10.1088/1751-8113/47/4/045204
Abstract: We 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.
ISSN: 1751-8113
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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