Approximation of Generalized Biaxisymmetric Potentials in $L^{\beta}$-norm

Abstract

Let $F$ be a real valued generalized biaxisymmetric potential (GBASP) in $L^{\beta}$ on $S_{R}$, the open sphere of radius $R$ about the origin. In this paper we have obtained the necessary and sufficient conditions on the rate of decrease of a sequence of best harmonic polynomial approximates to $F$ such that $F$ is harmonically continues as an entire function GBASP and determine their $(p,q)$-order and generalized $(p,q)$-type with respect to proximate order $\rho(r)$.