1 Ocak 2014 Dergi makalesi Açık Erişim

Pashaev, Oktay K.; Nalci, Sengul

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    <subfield code="a">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.</subfield>
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    <subfield code="a">Pashaev, Oktay K.</subfield>
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    <subfield code="a">10.1088/1751-8113/47/4/045204</subfield>
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    <subfield code="a">q-analytic functions, fractals and generalized analytic functions</subfield>
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