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AIMS Mathematics

2023, Volume 8, Issue 11: 26115-26133. doi: 10.3934/math.20231331
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Expansions of generalized bases constructed via Hasse derivative operator in Clifford analysis

  • 1.
    Mathematics Department, Faculty of Science, University of Assiut, Assiut 71516, Egypt
  • 2.
    Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
  • Received: 19 July 2023 Revised: 19 August 2023 Accepted: 27 August 2023 Published: 12 September 2023

  • MSC : 30G35, 41A10, 30D15

  • The present paper investigates the approximation of special monogenic functions (SMFs) in infinite series of hypercomplex Hasse derivative bases (HHDBs) in Fréchet modules (F-modules). The obtained results ensure the existence of such representation in closed hyperballs, open hyperballs, closed regions surrounding closed hyperballs, at the origin, and for all entire SMFs (ESMFs). Furthermore, we discuss the mode of increase (order and type) and the $ T_{\rho} $-property. This study enlightens several implications for some associated HHDBs, such as hypercomplex Bernoulli polynomials, hypercomplex Euler polynomials, and hypercomplex Bessel polynomials. Based on considering a more general class of bases in F-modules, our results enhance and generalize several known results concerning approximating functions in terms of bases in the complex and Clifford settings.

    Citation: Gamal Hassan, Mohra Zayed. Expansions of generalized bases constructed via Hasse derivative operator in Clifford analysis[J]. AIMS Mathematics, 2023, 8(11): 26115-26133. doi: 10.3934/math.20231331

    Related Papers:

  • The present paper investigates the approximation of special monogenic functions (SMFs) in infinite series of hypercomplex Hasse derivative bases (HHDBs) in Fréchet modules (F-modules). The obtained results ensure the existence of such representation in closed hyperballs, open hyperballs, closed regions surrounding closed hyperballs, at the origin, and for all entire SMFs (ESMFs). Furthermore, we discuss the mode of increase (order and type) and the $ T_{\rho} $-property. This study enlightens several implications for some associated HHDBs, such as hypercomplex Bernoulli polynomials, hypercomplex Euler polynomials, and hypercomplex Bessel polynomials. Based on considering a more general class of bases in F-modules, our results enhance and generalize several known results concerning approximating functions in terms of bases in the complex and Clifford settings.


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