Approximation by Entire Functions on a Countable Set of Continua

N. A. Shirokov, O. V. Silvanovich

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

Abstract: The problem of approximation by entire functions of exponential type defined on a countable set E of continua Gn, E = $$\bigcup\nolimits_{n \in \mathbb{Z}} {{{G}_{n}}} $$ is considered in this paper. It is assumed that all Gn are pairwise disjoint and are situated near the real axis. It is also assumed that all Gn are commensurable in a sense and have uniformly smooth boundaries. A function f is defined independently on each Gn and is bounded on E and f (r) has a module of continuity ω which satisfies condition $$\int\limits_0^x {\frac{{\omega (t)}}{t}dt} + x\int\limits_x^\infty {\frac{{\omega (t)}}{{{{t}^{2}}}}dt} \leqslant c\omega (x).$$An entire function Fσ of exponential type ≤σ is then constructed so that the following estimate of approximation of the function f by functions Fσ is valid: $$\left| {f(z) - {{F}_{\sigma }}(z)} \right| \leqslant {{c}_{f}}{{\sigma }^{{ - r}}}\omega ({{\sigma }^{{ - r}}}),\quad z \in \mathbb{Z},\quad \sigma \geqslant 1.$$

Язык оригиналаанглийский
Страницы (с-по)329-335
Число страниц7
ЖурналVestnik St. Petersburg University: Mathematics
Том53
Номер выпуска3
DOI
СостояниеОпубликовано - 1 июл 2020

Предметные области Scopus

  • Математика (все)

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