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Citation - WoS: 7
Citation - Scopus: 8
Q-Analytic Functions, Fractals and Generalized Analytic Functions
(IOP Publishing Ltd., 2014) Pashaev, Oktay; Nalcı, Şengül
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.

Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection