D. Kumar, H.S. Kasana
On the approximation of entire functions over Carath\'eodory domains

Comment.Math.Univ.Carolinae 35,4 (1994) 681-689.

Abstract:Let $D$ be a Carath\'eodory domain. For \text {$1\leq p\leq \infty $}, let $L^p(D)$ be the class of all functions $f$ holomorphic in $D$ such that $\|f\|_{D,p}=[\frac {1}{A}\int \int _{D}^{}|f(z)|^p dx dy]^{1/p}<\infty $, where $A$ is the area of $D$. For $f\in L^p(D)$, set $$ E_n^p(f)=\inf _{t\in \pi _n} \|f-t\|_{D,p} ; $$ $\pi _n$ consists of all polynomials of degree at most $n$. In this paper we study the growth of an entire function in terms of approximation error in $L^p$-norm on $D$.

Keywords: approximation error, generalized parameters, $L^p$ norm and Fourier coefficients
AMS Subject Classification: Primary 30D15; Secondary 30E10