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http://hdl.handle.net/11701/5905
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Поле DC | Значение | Язык |
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dc.contributor.author | Silvanovich, Olga V. | - |
dc.contributor.author | Shirokov, Nikolai A. | - |
dc.date.accessioned | 2017-01-05T18:10:14Z | - |
dc.date.available | 2017-01-05T18:10:14Z | - |
dc.date.issued | 2016-12 | - |
dc.identifier.citation | Silvanovich O.V., Shirokov N.A. Approximation by entire functions on a countable union of segments on the real axis. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 4, pp. 644–650. | en_GB |
dc.identifier.other | 10.21638/11701/spbu01.2016.414 | - |
dc.identifier.uri | http://hdl.handle.net/11701/5905 | - |
dc.description.abstract | We state in the present paper a theorem about approximation of a function defined on a countable union of segments of the real line by means of entire functions of exponential type. The approximating function is supposed to belong to a Holder class α, 0 < α< 1, and the rate of approximation turns out to be better in a vicinity of ends of segments similary to the case of case of polynomial approximation of a function on one segment. Now, we consider a set E ⊂ R consisting of disjonct segments [an, bn], −∞ < n < +∞ such that bn − an bk − ak for any n and k and an+1 − bn bn − an for any n. The function f defined on E supposed to be bounded by a constant M on all of segments [an, bn] and satisfying the condition |f(x) − f(y)| ≤ c0|x − y|α, x, y ∈ [an, bn], 0 < α < 1. For σ ≥ 1, ξ = 1 σ , x ∈ [an, bn] we define a scale of approximation d1+ξ(x, [an, bn]) such that d1+ξ(x, [an, bn]) ξ(ξ2 + min(x − an)2, (bn − x)2) 1 2 . Then the main theorem states that there exists a constant c1 depending only on f and E such that we can find a function Fσ of exponential type ≤ σ which approximate a function f in a following way: |Fσ(x) − f(x)| ≤ c1dα 1+ξ(x, [an, bn]), x ∈ [an, bn]. Refs 4. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 4 | - |
dc.subject | Holder classe σ | en_GB |
dc.subject | entire function of exponential type | en_GB |
dc.subject | approximation on subsets of real line | en_GB |
dc.title | Approximation by entire functions on a countable union of segments on the real axis | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 4 |
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14-Silvanovich.pdf | 242,43 kB | Adobe PDF | Просмотреть/Открыть |
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