$L^p$-Approximation of generalized biaxially symmetric potentials over Carathéodory domains

Rok, strany: 2005, 563 - 572

Let $F^α,β$ be a real generalized biaxially symmetric potentials (GBASP) defined on the Carathéodory domain and let $L^p(D)$ be the class of functions $F^α,β$ holomorphic in $D$ such that $|F^α,β|_D,p=(A^-1\iint\limits_D|F^α,β| d xd y)^1/p$, $A$ is the area of the domain $D$. For $F^α,β\in L^p(D)$, set $E_n^p(F^α,β)=\inf\{|F^α,β- P^α,β|_D,p: P^α,β\in H_n\}$, $H_n$ consists of all even biaxially symmetric harmonic polynomials of degree at most $2n$. This paper deals with the growth of entire function GBASP in terms of approximation error in $L^p$@-norm on $D$. The analysis utilizes the Bergman and Gilbert integral operator method to extend results from classical function theory on the best polynomial approximation of analytic functions of a complex variable.

ISO 690:

Kasana, H., Kumar, D. 2005. $L^p$-Approximation of generalized biaxially symmetric potentials over Carathéodory domains. In Mathematica Slovaca, vol. 55, no.5, pp. 563-572. 0139-9918.

APA:

Kasana, H., Kumar, D. (2005). $L^p$-Approximation of generalized biaxially symmetric potentials over Carathéodory domains. Mathematica Slovaca, 55(5), 563-572. 0139-9918.