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Ukrainian Mathematical Journal

, Volume 46, Issue 9, pp 1235–1247 | Cite as

On the best polynomial approximation of entire transcendental functions in banach spaces. I

  • S. B. Vakarchuk
Article

Abstract

We study the behavior of the best approximationsE n (ϕ) p of entire transcendental functions ϕ(z) of the order ρ=∞ by polynomials of at mostn th degree in the metric of the Banach space E′p(Ω) of functions /tf(z) analytic in a bounded simply connected domain Ω with rectifiable Jordan boundary and such that
$$\left\| f \right\|_{E'_p } = \left\{ {\iint_\Omega {\left| {f\left( z \right)} \right|^p }dxdy} \right\}^{{1 \mathord{\left/ {\vphantom {1 p}} \right. \kern-\nulldelimiterspace} p}}< \infty $$
.

In particular, we describe the relationship between the best approximationsE n (ϕ)p and theq-order andq-type of the function ϕ(z).

Keywords

Banach Space Polynomial Approximation Connected Domain Transcendental Function Entire Transcendental Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • S. B. Vakarchuk
    • 1
  1. 1.Institute of Geotechnical MechanicsUkrainian Academy of SciencesDnepropetrovsk

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