On the best polynomial approximation of entire transcendental functions in banach spaces. I |
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Authors: | S B Vakarchuk |
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Institution: | 1. Institute of Geotechnical Mechanics, Ukrainian Academy of Sciences, Dnepropetrovsk
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Abstract: | We study the behavior of the best approximationsE n (?) p of entire transcendental functions ?(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 (?)p and theq-order andq-type of the function ?(z). |
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