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Sbornik: Mathematics, 2018, Volume 209, Issue 7, Pages 958–984
DOI: https://doi.org/10.1070/SM8758 (Mi sm8758) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Extremal problems in nonquasianalytic Carleman classes. Applications

A. M. Gaisinab

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
b Bashkir State University, Ufa
English version PDF (648 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM8758
Abstract: An extremal problem is considered in the family of functions in a nonquasianalytic Carleman class on a closed interval that vanish together with all derivatives at a point in this interval. Applications to approximation theory and, in particular, to a system of exponentials with exponents satisfying the Fejér (or Levinson) condition are indicated; an asymptotic estimate as $\delta\to 0$ is obtained for the distance in $C_{[0,\delta]}$ between a fixed exponential and the closure of the linear span of other elements of this system.
Bibliography: 25 titles.
Keywords: nonquasianalytic Carleman class, extremal problem, minimal system of exponentials.
Funding agency Grant number
Russian Foundation for Basic Research 17-41-020070 р_а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 17-41-020070 p_a).
Received: 16.06.2016 and 15.06.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 7, Pages 44–70
DOI: https://doi.org/10.4213/sm8758
Bibliographic databases:
Document Type: Article
UDC: 517.53+ 517.518.25
MSC: 30B60, 30D60
Language: English
Original paper language: Russian
Citation: A. M. Gaisin, “Extremal problems in nonquasianalytic Carleman classes. Applications”, Mat. Sb., 209:7 (2018), 44–70; Sb. Math., 209:7 (2018), 958–984
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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