Entire functions of order 1/2 in the approximation to functions on a semiaxis

O.V. Silvanovich, N. A. Shirokov

Результат исследований: Научные публикации в периодических изданияхстатья

1 Цитирования (Scopus)


We present a theorem in the present paper on an approximation to functions of a Hölder class on a countable union of segments lying on a positive ray by entire functions of order 1/2 bounded on this ray. Problems related to the approximation of entire functions on subsets of the semiaxis by using entire functions of order 1/2 are closely related to problems of approximating functions on subsets of the whole axis using entire functions of exponential type but have their own specifics. We consider segments In in this paper with lengths of order n such that the distance between In and In + 1 is also of order n. Cases of the whole semiaxis or the union of finitely many segments and a ray were considered in previous papers. As for the problem of approximating functions of the Hölder class on the union of a countable set of segments on the whole axis, it turns out that the approximation rate at neighborhoods of the segment endpoints as the type of the functions increases is higher than that in a neighborhood of their midpoints.
Язык оригиналаанглийский
Страницы (с-по)394-400
ЖурналVestnik St. Petersburg University: Mathematics
Номер выпуска4
Ранняя дата в режиме онлайн23 дек 2019
СостояниеОпубликовано - 2019

Предметные области Scopus

  • Математика (все)

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