Ruscheweyh Differential Operator Sets of Basic Sets of Polynomials of Several Complex Variables in Hyperelliptical Regions
نویسنده
چکیده
The idea of the basic sets of polynomials of one complex variable appeared in 1930’s by Whittaker [33,34,35] who laid down the definition of a basic sets and their effectiveness. The study of the basic sets of polynomials of several complex variables was initiated by Mursi and Makar [25,26], Nassif [27], Kishka and others [13,14,17,18,19], where the representation in polycylindrical and hyperspherical regions was considered. Also, there are studies on basic sets of polynomials such as in Clifford Analysis [1,2,3,4,5,6,7,8] and in Faber regions [11,28,31,32]. The problem of derived and integrated sets of basic sets of polynomials in one and two complex variables was studied by many authors [9,10,20,21,23,24], where they considered the unit disk ∆ = {z : |z| < 1} in the complex plane C, circles and hyperspherical regions. Recently, in [12], the author studied this problem in a new region which is called hyperelliptical region. The purpose of this paper is to establish the effectiveness of Ruscheweyh differential operator sum and product sets of basic sets of polynomials of several complex variables in an open hyperellipse, in a closed hyperellipse and in the regions D(E[r]) which means unspecified domain containing the closed hyperellipse E[r]. These results extend my results concerning the effectiveness in hyperspherical regions found in [15].
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تاریخ انتشار 2007