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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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On approximation processes defined by a cosine operator function; pp 214–224

(Full article in PDF format) https://doi.org/10.3176/proc.2017.2.11


Authors

Andi Kivinukk, Anna Saksa, Maria Zeltser

Abstract

In this paper we introduce the Blackman- and Rogosinski-type approximation processes in an abstract Banach space setting. The historical roots of these processes go back to W. W. Rogosinski in 1926. The given new definitions use a cosine operator functions concept. We prove that in the presented setting the Blackman- and Rogosinski-type operators possess the order of approximation that coincides with results known in trigonometric approximation. Also applications for different types of approximations are given. An application for the Fourier series of symmetric functions with respect to η is emphasized.

Keywords

cosine operator function, Blackman-type approximation processes, Rogosinski-type approximation processes, modulus of continuity, Fourier series of symmetric functions with respect to η

References

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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December