On the approximation of entire functions over Carathéodory domains

Kumar, Devendra, and Kasana, Harvir S.. "On the approximation of entire functions over Carathéodory domains." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 681-689. <http://eudml.org/doc/247619>.

@article{Kumar1994,
abstract = {Let $D$ be a Carathéodory domain. For $1\le p\le \infty $, let $L^p(D)$ be the class of all functions $f$ holomorphic in $D$ such that $\Vert f\Vert _\{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 \[ E\_n^p(f)=\inf \_\{t\in \pi \_n\} \Vert f-t\Vert \_\{D,p\}\,; \]$\pi _n$ 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 $D$.},
author = {Kumar, Devendra, Kasana, Harvir S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {approximation error; generalized parameters; $L^p$ norm and Fourier coefficients},
language = {eng},
number = {4},
pages = {681-689},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the approximation of entire functions over Carathéodory domains},
url = {http://eudml.org/doc/247619},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Kumar, Devendra
AU - Kasana, Harvir S.
TI - On the approximation of entire functions over Carathéodory domains
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 681
EP - 689
AB - Let $D$ be a Carathéodory domain. For $1\le p\le \infty $, let $L^p(D)$ be the class of all functions $f$ holomorphic in $D$ such that $\Vert f\Vert _{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 \[ E_n^p(f)=\inf _{t\in \pi _n} \Vert f-t\Vert _{D,p}\,; \]$\pi _n$ 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 $D$.
LA - eng
KW - approximation error; generalized parameters; $L^p$ norm and Fourier coefficients
UR - http://eudml.org/doc/247619
ER -