RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 4(1), Pages 413–422 (Mi isu530)  

Mathematics

Discrete Transform with Stick Property Based on $\{\sin x\sin kx\}$ and Second Kind Chebyshev Polynomials Systems

I. I. Sharapudinov, G. G. Akniev

Daghestan Scientific Centre Of Russian Academy of Sciences, 45, Gadgieva str., Makhachkala, Republic of Dagestan, 367000, Russia

Abstract: In this paper we introduce the discrete series with the «sticking»-property of the periodic ($\{\sin x \sin kx\}$ system) and non-periodic (using the system of the second kind of Chebyshev polynomials $U_k(x)$) cases. It is shown that series of the system $\{\sin x \sin kx\}$ have an advantage over cosine Fourier series because they have better approximation properties near the bounds of the $[0,\pi]$ segment. Similarly discrete series of the system $U_k(x)$ near the bound of the $[-1,1]$ approximates given function significantly better than Fouries sums of Chebyshev polynomials.

Key words: approximation theory, Fouries series, special series, piecewise approximation.

DOI: https://doi.org/10.18500/1816-9791-2014-14-4-413-422

Full text: PDF file (195 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.538

Citation: I. I. Sharapudinov, G. G. Akniev, “Discrete Transform with Stick Property Based on $\{\sin x\sin kx\}$ and Second Kind Chebyshev Polynomials Systems”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(1) (2014), 413–422

Citation in format AMSBIB
\Bibitem{ShaAkn14}
\by I.~I.~Sharapudinov, G.~G.~Akniev
\paper Discrete Transform with Stick Property Based on $\{\sin x\sin kx\}$ and Second Kind Chebyshev Polynomials Systems
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(1)
\pages 413--422
\mathnet{http://mi.mathnet.ru/isu530}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-4-413-422}
\elib{https://elibrary.ru/item.asp?id=22575450}


Linking options:
  • http://mi.mathnet.ru/eng/isu530
  • http://mi.mathnet.ru/eng/isu/v14/i4/p413

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
    Number of views:
    This page:189
    Full text:73
    References:26

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020