Best weighted approximation of some kernels on the real axis

S.O. Chaichenko; V.V. Savchuk; A.L. Shydlich

doi:10.15421/242513

Best weighted approximation of some kernels on the real axis

S.O. Chaichenko (Donbas State Pedagogical University), https://orcid.org/0000-0002-2724-8749
V.V. Savchuk (Institute of Mathematics of NAS of Ukraine), https://orcid.org/0000-0002-6713-4471
A.L. Shydlich (Institute of Mathematics of the NAS of Ukraine, National University of Life and Environmental Sciences of Ukraine), https://orcid.org/0000-0002-6421-9277

Abstract

We calculate the exact value and find the polynomial of the best weighted polynomial approximation of kernels of the form $$$\frac {A+Bt}{(t^2+\lambda^2)^{s+1}}$$$, where $$$A$$$ and $$$B$$$ are fixed complex numbers, $$$\lambda>0$$$, $$$s\in {\mathbb N}$$$, in the mean square metric.

Keywords

Takenaka-Malmqvist system; Blaschke product; best weighted approximation

MSC 2020

Pri 41A10, Sec 30J10, 41A81

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