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Mat. Zametki, 1997, Volume 62, Issue 6, Pages 871–880 (Mi mz1676)  

This article is cited in 9 scientific papers (total in 9 papers)

Estimates of polynomials orthogonal with respect to the Legendre–Sobolev inner product

F. Marcellana, B. P. Osilenkerb

a Carlos III University of Madrid
b Moscow State University of Civil Engineering

Abstract: For the Legendre–Sobolev orthonormal polynomials $\widehat B_n(x)=\widehat B_n(x;M,N)$ depending on the parameters $M\ge0$, $N\ge0$, weighted and uniform estimates on the orthogonality interval are obtained. It is shown that, unlike the Legendre orthonormal polynomials, the polynomials $\widehat B_n(x)$ for $M>0$, $N>0$ decay at the rate of $n^{-3/2}$ at the points 1 and -1. The values of $\widehat B'_n(\pm1)$ are calculated.

DOI: https://doi.org/10.4213/mzm1676

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English version:
Mathematical Notes, 1997, 62:6, 731–738

Bibliographic databases:

UDC: 517.538.3
Received: 02.04.1996

Citation: F. Marcellan, B. P. Osilenker, “Estimates of polynomials orthogonal with respect to the Legendre–Sobolev inner product”, Mat. Zametki, 62:6 (1997), 871–880; Math. Notes, 62:6 (1997), 731–738

Citation in format AMSBIB
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\paper Estimates of polynomials orthogonal with respect to the Legendre--Sobolev inner product
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\yr 1997
\vol 62
\issue 6
\pages 871--880
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\jour Math. Notes
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\vol 62
\issue 6
\pages 731--738
\crossref{https://doi.org/10.1007/BF02355461}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Moreno, AF, “Estimates for polynomials orthogonal with respect to some Gegenbauer-Sobolev type inner product”, Journal of Inequalities and Applications, 3:4 (1999), 401  crossref  mathscinet  isi
    2. Osilenker, BP, “Generalized trace formula and asymptotics of the averaged Turan determinant for polynomials orthogonal with a discrete Sobolev inner product”, Journal of Approximation Theory, 141:1 (2006), 70  crossref  mathscinet  zmath  isi  scopus  scopus
    3. B. P. Osilenker, “An Extremal Problem for Algebraic Polynomials in the Symmetric Discrete Gegenbauer–Sobolev Space”, Math. Notes, 82:3 (2007), 366–379  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Fejzullahu, BX, “A COHEN TYPE INEQUALITY FOR LEGENDRE-SOBOLEV EXPANSIONS”, Filomat, 22:1 (2008), 23  crossref  mathscinet  zmath  isi
    5. B. P. Osilenker, “Some extremal problems for algebraic polynomials in loaded spaces”, Russian Math. (Iz. VUZ), 54:2 (2010), 46–56  mathnet  crossref  mathscinet  zmath
    6. Alfaro M., Van Assche W., “Life and Work (So Far) of Paco Marcellan”, Recent Advances in Orthogonal Polynomials, Special Functions, and their Applications, Contemporary Mathematics, 578, eds. Arvesu J., Lagomasino G., Amer Mathematical Soc, 2011, 1–18  crossref  mathscinet  isi
    7. Osilenker B.P., “O ryadakh fure po simmetrichnym ortogonalnym polinomam gegenbauera - soboleva”, Vestnik MGSU, 2011, no. 4, 74–74  elib
    8. Marcellan F. Quintana Ya. Urieles A., “On W-1,W-P-Convergence of Fourier-Sobolev Expansions”, J. Math. Anal. Appl., 398:2 (2013), 594–599  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Marcellan F. Quintana Ya. Urieles A., “On the Pollard Decomposition Method Applied to Some Jacobi-Sobolev Expansions”, Turk. J. Math., 37:6 (2013), 934–948  crossref  mathscinet  zmath  isi  scopus  scopus
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