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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 | 2017-07-05T09:09:37Z | - |
dc.date.available | 2017-07-05T09:09:37Z | - |
dc.date.issued | 2017-03 | - |
dc.identifier.citation | Silvanovich O.V., Shirokov N.A. Approximation by entire functions on a countable union of segments on the real axis. 2. Proof of the main theorem. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 1, pp. 53–63. | en_GB |
dc.identifier.other | 10.21638/11701/spbu01.2017.108 | - |
dc.identifier.uri | http://hdl.handle.net/11701/6687 | - |
dc.description.abstract | We proof 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. The set E ⊂ R consists of disjoint 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 and satisfying the condition |f(x) − f(y)| ≤ c0|x − y| , x, y ∈ [an, bn], 0 < α < 1. The construction of an approximation of f by entire functions we begin from a construction of a series of domains D+ and D− depending of sequens {x′}n∈Z and {x′′}n∈Z : x′ n, x′′ n ∈ [an, bn]. We introduce a special conformed mappings of D+ and D− to themselves and use these mapping to form kernels Rk(z,w, ξ, ζ). Afterwards we combine a continuation of a function f from the set E to the whole complex plane C from our first part of this paper and kernels Rk(z,w, ξ, ζ). We get as a result a series of entire functions of exponential type depending on sequences {x′ n}n∈Z and {x′′ n}n∈Z. Then we use sequences {x′ n}n∈Z and {x′′ n}n∈Z to construct a final approximating entire function F . Refs 3. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 4 (62); Issue 1 | - |
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. 2. Proof of the main theorem | en_GB |
dc.type | Article | en_GB |
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