×

On the approximation of entire functions over Carathéodory domains. (English) Zbl 0815.30019

Let \(D\) be a domain. For \(1\leq p\leq \infty\), let \(L^ p(D)\) be the set of all functions \(f\) holomorphic in \(D\) such that \[ \| f\|_{D,p}= \left[ {1\over A} \iint_ D | f(z)|^ p dx dy\right]^{1/p}< \infty, \] where \(A\) is the area of \(D\). For \(L^ p(D)\) set \(E^ p_ n(f)\) the best approximation of \(f\in L^ p(D)\) by polynomials of degree \(\leq n\) in the norm \(\| f\|_{D,p}\). In this paper the authors study the growth of the entire functions in terms of \(E^ p_ n(f)\).

MSC:

30D15 Special classes of entire functions of one complex variable and growth estimates
30E10 Approximation in the complex plane
PDFBibTeX XMLCite
Full Text: EuDML