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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2016, Volume 16, Issue 1, Pages 34–41 (Mi isu619)  

Mathematics

Special wavelets based on Chebyshev polynomials of the second kind and their approximative properties

M. S. Sultanakhmedov

Daghestan Scientific Center of RAS, 45, Gadzhiev st., Makhachkala, Daghestan, Russia, 367000

Abstract: The system of wavelets and scalar functions based on Chebyshev polynomials of the second kind and their zeros is considered. With the help of them we construct a complete orthonormal system of functions. A certain disadvantage is shown in approximation properties of partial sums of the corresponding wavelet series, related to the properties of Chebyshev polynomials themselves and meaning a significant decrease of the rate of their convergence to the original function at the endpoints of orthogonality segment. As an alternative, we propose a modification of Chebyshev wavelet series of the second kind by analogy to the special polynomial series with the property of adhesion. These new special wavelet series is proved to be deprived of the mentioned disadvantage and to have better approximative properties.

Key words: polynomial wavelets, special wavelet series, Chebyshev polynomials of the second kind, function approximation.

DOI: https://doi.org/10.18500/1816-9791-2016-16-1-34-41

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UDC: 517.51

Citation: M. S. Sultanakhmedov, “Special wavelets based on Chebyshev polynomials of the second kind and their approximative properties”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:1 (2016), 34–41

Citation in format AMSBIB
\Bibitem{Sul16}
\by M.~S.~Sultanakhmedov
\paper Special wavelets based on Chebyshev polynomials of the second kind and their approximative properties
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2016
\vol 16
\issue 1
\pages 34--41
\mathnet{http://mi.mathnet.ru/isu619}
\crossref{https://doi.org/10.18500/1816-9791-2016-16-1-34-41}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3501502}
\elib{https://elibrary.ru/item.asp?id=25897435}


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  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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