1 Ocak 2014 Dergi makalesi Açık Erişim

Pashaev, Oktay K.; Nalci, Sengul

Citation Style Language JSON

{
  "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.", 
  "author": [
    {
      "family": "Pashaev", 
      "given": " Oktay K."
    }, 
    {
      "family": "Nalci", 
      "given": " Sengul"
    }
  ], 
  "container_title": "JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL", 
  "id": "67095", 
  "issue": "4", 
  "issued": {
    "date-parts": [
      [
        2014, 
        1, 
        1
      ]
    ]
  }, 
  "title": "q-analytic functions, fractals and generalized analytic functions", 
  "type": "article-journal", 
  "volume": "47"
}