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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 162, Pages 57–61 (Mi into441)  
This article is cited in 1 scientific paper (total in 1 paper)

Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces

I. Kh. Musinab

a Bashkir State University, Ufa
b Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa
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Abstract: By a given family of convex functions on the real axis that grow at infinity faster than any linear function and by a certain logarithmically convex sequence of positive numbers, we construct the space of infinitely differentiable functions on the real line. Under the condition of a logarithmic gap between weight functions, we prove the possibility of approximation by polynomials in this space.
Keywords: Fourier–Laplace transform, entire function, convex function, Young–Fenchel transform.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 257, Issue 3, Pages 329–333
DOI: https://doi.org/10.1007/s10958-021-05486-0
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 41A10
Language: Russian
Citation: I. Kh. Musin, “Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 57–61; J. Math. Sci. (N. Y.), 257:3 (2021), 329–333
Citation in format AMSBIB
\Bibitem{Mus19}
\by I.~Kh.~Musin
\paper Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces
\inbook Complex Analysis. Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 162
\pages 57--61
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into441}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3981817}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 257
\issue 3
\pages 329--333
\crossref{https://doi.org/10.1007/s10958-021-05486-0}
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    Citing articles in Google Scholar: Russian citations, English citations
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