Abstract
In this paper, it is shown that certain classes of regular functions of several complex variables be represented by exponential sets of polynomials in hyperelliptical regions. Moreover, an upper bound for the order of exponential set is given.
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Abul-Ez M.: Inverse sets of polynomials in Clifford analysis. Arch. der Math. 58, 561–567 (1992)
Abul-Ez M., Constales D.: Similar functions and similar bases of polynomials in Clifford setting. Complex Variables 48, 1055–1070 (2003)
Abul-Ez, M., Saleem, M., Zayed, M.: On the representation near a point of Clifford valued functions by infinite series of polynomials. In: 9th International Conferenceon Clifford Algebras, Weimar, Germany, 15–20 July (2011)
Abul-Ez M., Morais J., Zayed M.: Generalized derivative and primitive of Cliffordian bases of polynomials constructed through Appell monomials. Comput. Meth. Func. Theo. 4, 501–515 (2012)
Abul-Ez M., Saleem M., Abd-Elmageed H., Morais J.: On polynomial series expansions of Cliffordian functions in open balls and at the origin. Cliff. Anal. Cliff. Alge. Appl. 2, 291–307 (2012)
Abul-Ez M., Constales D.: On the order of basic series representing Clifford valued functions. Appl. Math. Comput. 142, 575–584 (2003)
Cannon B.: On the convergence of series of polynomials. Proc. Lond. Math. Soc. 43, 348–364 (1937)
Cannon B.: On the representation of integral functions by general basic series. Math. Zeit. 45, 185–208 (1939)
El-Sayed A.: On derived and integrated sets of basic sets of polynomials of several complex variables. Acta Math. Acad. Paed. Nyiregyhazi 19, 195–204 (2003)
El-Sayed, A., Kishka, Z.M.G.: On the effectiveness of basic sets of polynomials of several complex variables in elliptical regions. In: Proceedings of the 3rd International ISAAC Congress, pp. 265-278. Freie Universitaet Berlin, Germany. Kluwer, Dordrecht (2003)
Hassan G.F.: Ruscheweyh differential operator sets of basic sets of polynomials of several complex variables in hyperelliptical regions. Acta Math. Acad. Paed. Nyiregyhazi 22, 247–264 (2006)
Kishka Z.M.G.: On the convergence of properties of basic sets of polynomials of several complex variables i. Sohg Pure, Appl. Sci. Bull. Fac. Sci. Assiut Univ. 7, 71–119 (1991)
Kishka Z.M.G.: Power set of simple set of polynomials of two complex variables. Bull. Soc. R. Sci. Liege 62, 265–278 (1993)
Kishka Z.M.G, El-Sayed A.: On the order and type of basic and composite sets of polynomials in complete Reinhardt domains. Period. Math. Hung. 46, 67–79 (2003)
Mursi, M., Maker, B.H.: Basic sets of polynomials of several complex variables i. In: The Second Arab Sci. Congress, pp. 51–60. Cairo (1955)
Mursi, M., Maker, B.H.: Basic sets of polynomials of several complex variables ii. In: The Second Arab Sci. Congress, pp. 61–68, Cairo (1955)
Nassif M.: Composite sets of polynomials of several complex variables. Publ. Math. Debrecen 18, 43–52 (1971)
Sayyed K.A.M., Metwally M.S., Hassan G.F.: Effectiveness of equivalent sets of polynomials of two complex variables in polycylinders and Faber regions. Int. J. Math. Math. Sci. 2, 529–539 (2000)
Whittaker J.M.: On series of polynomials. Quart. J. Math. Oxford 5, 224–239 (1934)
Whittaker, J.M.: Sur les series de base de polynomes quelconques. Gauthier-Villars, Paris (1949)
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Kishka, Z.G., Saleem, M.A. & Abul-Dahab, M.A. On Simple Exponential Sets of Polynomials. Mediterr. J. Math. 11, 337–347 (2014). https://doi.org/10.1007/s00009-013-0296-7
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DOI: https://doi.org/10.1007/s00009-013-0296-7