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


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).


Banach Space Polynomial Approximation Connected Domain Transcendental Function Entire Transcendental Function 
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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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