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- W1980045101 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." @default.
- W1980045101 created "2016-06-24" @default.
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- W1980045101 date "2014-01-07" @default.
- W1980045101 modified "2023-09-24" @default.
- W1980045101 title "<i>q</i>-analytic functions, fractals and generalized analytic functions" @default.
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- W1980045101 doi "https://doi.org/10.1088/1751-8113/47/4/045204" @default.
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