Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Lukomskii S. F., Mushko M. D. On Binary B-splines of Second Order. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 2, pp. 172-182. DOI: 10.18500/1816-9791-2018-18-2-172-182, EDN: XQFNRB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.05.2018
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Russian
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Article
UDC: 
517.51
EDN: 
XQFNRB

On Binary B-splines of Second Order

Autors: 
Lukomskii Sergei Feodorovich, Saratov State University
Mushko Maxim D., Saratov State University
Abstract: 

The classical B-spline is defined recursively as the convolution Bn+1 = Bn ∗ B0, where B0 is the characteristic function of the unit interval. The classical B-spline is a refinable function and satisfies the Riesz inequality. Therefore any B-spline Bn generates the Riesz multiresolution analysis (MRA). We define binary B-splines, obtained by double integration of the third Walsh function. We give an algorithm for constructing an interpolating spline of the second degree for a binary node system and find the approximation order of this interpolation process. We also prove that the system of dilations and shifts of the constructed B-spline generates an MRA (Vn) in De Boor sense. This MRA is not Riesz. But we can find the approximation order of functions from the Sobolev spaces Ws 2 , s > 0 by the subspaces (Vn).

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Received: 
06.01.2018
Accepted: 
09.06.2018
Published: 
04.06.2018
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