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The growth of generalized Hadamard product of entire axially monogenic functions

Year 2018, Volume: 47 Issue: 5, 1231 - 1239, 16.10.2018

Abstract

In this article, we estimated upper bounds for the growth order and growth type of generalized Hadamard product entire axially monogenic functions. Also, some results concerning the linear substitution are discussed. The obtained results are the natural generalizations of those given in complex setting of one variable to higher dimensions of more than four.

References

  • Abul-Ez. M, Hadamard product of bases of polynomials in Clifford analysis, Complex Vari- ables., 43, 109-128, 2000.
  • Abul-Ez. M and Constales. D, Basic sets of polynomials in Clifford analysis, Complex Vari- ables., 14, 177-185, 1990.
  • Abul-Ez. M and Constales. D, Linear substitution for basic sets of polynomials in Clifford analysis, Portugaliae Mathematica., 48, 143-154, 1991.
  • Abul-Ez. M and Constales. D, On convergence properties of basic series representing special monogenic functions, Arch. Math., 81, 62-71, 2002.
  • Abul-Ez. M and De Almeida. R, On the lower order and type of entire axially monogenic functions, Results. Math., 63, 1257-1275, 2013.
  • Brackx. F, Delanghe. R and Sommen. F, Clifford analysis. Research Notes in Mathematics 76. London: London Pitman Books Ltd, 1982.
  • Constales. D, De Almeida. R and Krausshar. R, On the relation between the growth and the Taylor coeffcients of entire solutions to the higher dimensional Cauchy-Riemann system in $R^{n+1}$, J. Math. Anal. Appl., 327, 763-775, 2007.
  • Constales. D, De Almeida. R and Krausshar. R, On the growth type of entire monogenic functions, Arch. Math., 88, 153-163, 2007.
  • Constales. D, De Almeida. R and Krausshar. R, Applications of the maximum term and the central index in the asymptotic growth analysis of entire solutions to higher dimensional polynomial Cauchy-Riemann equations, Complex Var. Elliptic Equ., 53, 195-213, 2008.
  • De Almeida. R and Krausshar. R, Basics on growth orders of polymonogenic functions, Complex Var. Elliptic Equ., 60, 1-25, 2015.
  • Delanghe. R, Sommen. F and Souccěk. V, Clifford algebra and spinor-valued function. Dor- drecht: Kluwer Academic Publishers, 1992.
  • Dutta. R. K, On order of a function of several complex variables analytic in the unit polydisc, Krag. J. Math., 36, 163-174, 2012.
  • Gol'dberg. A. A, Elementary remarks on the formulas defining the order and type entire functions in several variables, Dokl. Akad. Nauk Arm. SSR., 29, 145-151, 1959.
  • Jae Hochoi. J and Kim. Y. C, Generalized Hadamard product functions with negative coefficients, J. Math. Anal. Appl., 199, 459-501, 1996.
  • Kishka. Z, Abul-Ez. M, Saleem. M and Abd-Elmaged. H, On the order and type of entire matrix functions in complete Reinhardt domain, J. Mod. Meth. Numer. Math., 3, 31-40, 2012.
  • Lounesto. P and Bergh. P, Axially symmetric vector fields and their complex potentials, Complex Variables., 2, 139- 150, 1983.
  • Ronkin. L. I, Introduction to the theory of entire functions of several variables, Trans. Math. Monog., 44. Providence R.I., American Mathematical Society, VI, 1974.
  • Sayyed. K, Metwally. M and Mohamed. M, Some order and type of generalized Hadamard product of entire functions, South. Asi. Bull. Math., 26, 121-132, 2002.
  • Sommen. F, Plane elliptic systems and monogenic functions in symmetric domains, Suppl. Rend. Circ. Mat. Palermo., 6, 259-269, 1984.
  • Srivastava. R. K and Kumar. V, On the order and type of integral functions of several complex variables, Compo. Math., 17, 161-166, 1966.
  • Srivastava. G. S and Kumar. S, On the generalized order and generalized type of entire monogenic functions, Demon. Math., 46, 663-677, 2013.
Year 2018, Volume: 47 Issue: 5, 1231 - 1239, 16.10.2018

Abstract

References

  • Abul-Ez. M, Hadamard product of bases of polynomials in Clifford analysis, Complex Vari- ables., 43, 109-128, 2000.
  • Abul-Ez. M and Constales. D, Basic sets of polynomials in Clifford analysis, Complex Vari- ables., 14, 177-185, 1990.
  • Abul-Ez. M and Constales. D, Linear substitution for basic sets of polynomials in Clifford analysis, Portugaliae Mathematica., 48, 143-154, 1991.
  • Abul-Ez. M and Constales. D, On convergence properties of basic series representing special monogenic functions, Arch. Math., 81, 62-71, 2002.
  • Abul-Ez. M and De Almeida. R, On the lower order and type of entire axially monogenic functions, Results. Math., 63, 1257-1275, 2013.
  • Brackx. F, Delanghe. R and Sommen. F, Clifford analysis. Research Notes in Mathematics 76. London: London Pitman Books Ltd, 1982.
  • Constales. D, De Almeida. R and Krausshar. R, On the relation between the growth and the Taylor coeffcients of entire solutions to the higher dimensional Cauchy-Riemann system in $R^{n+1}$, J. Math. Anal. Appl., 327, 763-775, 2007.
  • Constales. D, De Almeida. R and Krausshar. R, On the growth type of entire monogenic functions, Arch. Math., 88, 153-163, 2007.
  • Constales. D, De Almeida. R and Krausshar. R, Applications of the maximum term and the central index in the asymptotic growth analysis of entire solutions to higher dimensional polynomial Cauchy-Riemann equations, Complex Var. Elliptic Equ., 53, 195-213, 2008.
  • De Almeida. R and Krausshar. R, Basics on growth orders of polymonogenic functions, Complex Var. Elliptic Equ., 60, 1-25, 2015.
  • Delanghe. R, Sommen. F and Souccěk. V, Clifford algebra and spinor-valued function. Dor- drecht: Kluwer Academic Publishers, 1992.
  • Dutta. R. K, On order of a function of several complex variables analytic in the unit polydisc, Krag. J. Math., 36, 163-174, 2012.
  • Gol'dberg. A. A, Elementary remarks on the formulas defining the order and type entire functions in several variables, Dokl. Akad. Nauk Arm. SSR., 29, 145-151, 1959.
  • Jae Hochoi. J and Kim. Y. C, Generalized Hadamard product functions with negative coefficients, J. Math. Anal. Appl., 199, 459-501, 1996.
  • Kishka. Z, Abul-Ez. M, Saleem. M and Abd-Elmaged. H, On the order and type of entire matrix functions in complete Reinhardt domain, J. Mod. Meth. Numer. Math., 3, 31-40, 2012.
  • Lounesto. P and Bergh. P, Axially symmetric vector fields and their complex potentials, Complex Variables., 2, 139- 150, 1983.
  • Ronkin. L. I, Introduction to the theory of entire functions of several variables, Trans. Math. Monog., 44. Providence R.I., American Mathematical Society, VI, 1974.
  • Sayyed. K, Metwally. M and Mohamed. M, Some order and type of generalized Hadamard product of entire functions, South. Asi. Bull. Math., 26, 121-132, 2002.
  • Sommen. F, Plane elliptic systems and monogenic functions in symmetric domains, Suppl. Rend. Circ. Mat. Palermo., 6, 259-269, 1984.
  • Srivastava. R. K and Kumar. V, On the order and type of integral functions of several complex variables, Compo. Math., 17, 161-166, 1966.
  • Srivastava. G. S and Kumar. S, On the generalized order and generalized type of entire monogenic functions, Demon. Math., 46, 663-677, 2013.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

M. Abdalla This is me

M. Abul-ez This is me

Publication Date October 16, 2018
Published in Issue Year 2018 Volume: 47 Issue: 5

Cite

APA Abdalla, M., & Abul-ez, M. (2018). The growth of generalized Hadamard product of entire axially monogenic functions. Hacettepe Journal of Mathematics and Statistics, 47(5), 1231-1239.
AMA Abdalla M, Abul-ez M. The growth of generalized Hadamard product of entire axially monogenic functions. Hacettepe Journal of Mathematics and Statistics. October 2018;47(5):1231-1239.
Chicago Abdalla, M., and M. Abul-ez. “The Growth of Generalized Hadamard Product of Entire Axially Monogenic Functions”. Hacettepe Journal of Mathematics and Statistics 47, no. 5 (October 2018): 1231-39.
EndNote Abdalla M, Abul-ez M (October 1, 2018) The growth of generalized Hadamard product of entire axially monogenic functions. Hacettepe Journal of Mathematics and Statistics 47 5 1231–1239.
IEEE M. Abdalla and M. Abul-ez, “The growth of generalized Hadamard product of entire axially monogenic functions”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 5, pp. 1231–1239, 2018.
ISNAD Abdalla, M. - Abul-ez, M. “The Growth of Generalized Hadamard Product of Entire Axially Monogenic Functions”. Hacettepe Journal of Mathematics and Statistics 47/5 (October 2018), 1231-1239.
JAMA Abdalla M, Abul-ez M. The growth of generalized Hadamard product of entire axially monogenic functions. Hacettepe Journal of Mathematics and Statistics. 2018;47:1231–1239.
MLA Abdalla, M. and M. Abul-ez. “The Growth of Generalized Hadamard Product of Entire Axially Monogenic Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 5, 2018, pp. 1231-9.
Vancouver Abdalla M, Abul-ez M. The growth of generalized Hadamard product of entire axially monogenic functions. Hacettepe Journal of Mathematics and Statistics. 2018;47(5):1231-9.