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Izv. Saratov Univ. Math. Mech. Inform., 2018, Volume 18, Issue 2, Pages 172–182 (Mi isu753)  

Scientific Part
Mathematics

On binary B-splines of second order

S. F. Lukomskii, M. D. Mushko

Saratov State University, 83, Astrakhanskaya Str., Saratov, 410012, Russia

Abstract: The classical B-spline is defined recursively as the convolution $B_{n+1}=B_n*B_0$, where $B_0$ 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 $B_n$ 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 $ (V_n) $ in De Boor sense. This MRA is not Riesz. But we can find the approximation order of functions from the Sobolev spaces $W_2^s, s>0$ by the subspaces $ (V_n) $.

Key words: binary B-splines, multiresolution analysis, Sobolev spaces.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00152_а
This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00152).


DOI: https://doi.org/10.18500/1816-9791-2018-18-2-172-182

Full text: PDF file (208 kB)
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Bibliographic databases:

UDC: 517.51

Citation: S. F. Lukomskii, M. D. Mushko, “On binary B-splines of second order”, Izv. Saratov Univ. Math. Mech. Inform., 18:2 (2018), 172–182

Citation in format AMSBIB
\Bibitem{LukMus18}
\by S.~F.~Lukomskii, M.~D.~Mushko
\paper On binary B-splines of second order
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2018
\vol 18
\issue 2
\pages 172--182
\mathnet{http://mi.mathnet.ru/isu753}
\crossref{https://doi.org/10.18500/1816-9791-2018-18-2-172-182}
\elib{https://elibrary.ru/item.asp?id=35085047}


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