Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Novikov V. V. Interpolation of Continuous in Ordered H-variation Functions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 4, pp. 418-421. DOI: 10.18500/1816-9791-2015-15-4-418-422

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
21.12.2015
Full text:
(downloads: 90)
Language: 
Russian
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UDC: 
517.51

Interpolation of Continuous in Ordered H-variation Functions

Autors: 
Novikov Vladimir Vasil’evich, Engels' Technology Institute, Branch of Saratov State Technical University
Abstract: 

In 1972 D. Vaterman introduced a class of functions of Λ-bounded variation (in particular, a harmonic variation or an H-variation). Later he introduced also the class of functions of ordered ¤-bounded variation and the class of continuous in Λ-variation functions. These classes have been used by many authors in studies on the convergence and summability of the Fourier series. This paper investigates the behavior of the Lagrange interpolation of continuous in orderedH-variation functions.We prove a result: if f ∈ C2π is continuous in ordered harmonic variation on [−π,π], then the Lagrange trigonometric polynomials {Ln(f, x)} based on equidistant nodes converge to f uniformly on R.

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