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Zbl 0860.42003
Delvos, F.-J.
Approximation properties of periodic interpolation by translates of one function. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 28, No.2, 177-188 (1994). ISSN 0764-583X

Summary: In [J. Approx. Theory 1, 26-65 (1968; Zbl 0185.30901)] {\it M. Golomb} derived a Hilbert space approach to periodic splines of odd degree on uniform meshes, which were studied systematically for the first time by {\it W. Quade} and {\it L. Collatz} [Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl. 1938, 383-429 (1938; Zbl 0021.39701)]. Golomb's approach has been extended to more general methods of periodic interpolation by translates of a given periodic function $g$. It is the objective of this paper to investigate approximation properties of these interpolation methods in spaces of periodic functions which are closely related to $g$ and extend our previous results [in A. Haar Mem. Conf., Budapest/Hung. 1985, Colloq. Math. Soc. János Bolyai 49, 273-287 (1987; Zbl 0638.42003)]. As an application approximation properties of periodic splines of even degree are obtained.

MSC 2000:: *42A15 Trigonometric interpolation
41A05 Interpolation

Keywords: periodic splines; periodic interpolation

Citations: Zbl 0185.30901; Zbl 0021.39701; Zbl 0638.42003

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