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Mat. Sb., 2001, Volume 192, Number 3, Pages 115–136 (Mi msb553)  

This article is cited in 8 scientific papers (total in 8 papers)

Orthogonal polynomial Schauder bases in $C[-1,1]$ with optimal growth of degrees

M. A. Skopina

Saint-Petersburg State University

Abstract: For each $\varepsilon>0$ an orthogonal Schauder basis of algebraic polynomials $P_n$ in $C[-1,1]$ is constructed such that the degrees of the polynomials have the estimate $n(1+\varepsilon)$. This growth rate is the lowest possible.

DOI: https://doi.org/10.4213/sm553

Full text: PDF file (345 kB)
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English version:
Sbornik: Mathematics, 2001, 192:3, 433–454

Bibliographic databases:

UDC: 517.5
MSC: Primary 46E15, 42C40; Secondary 46C05, 42A16, 42A45
Received: 15.02.1999 and 28.12.2000

Citation: M. A. Skopina, “Orthogonal polynomial Schauder bases in $C[-1,1]$ with optimal growth of degrees”, Mat. Sb., 192:3 (2001), 115–136; Sb. Math., 192:3 (2001), 433–454

Citation in format AMSBIB
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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. A. Askari-Hemmat, M. A. Dehghan, M. A. Skopina, “Polynomial Wavelet-Type Expansions on the Sphere”, Math. Notes, 74:2 (2003), 278–285  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Hemmat A.A., Dehghan M.A., Skopina M., “Ridge wavelets on the ball”, J. Approx. Theory, 136:2 (2005), 129–139  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Moncayo, M, “A recursive procedure to obtain a class of orthogonal polynomial wavelets”, Mathematics and Computers in Simulation, 77:2–3 (2008), 266  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Obermaier, J, “Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel”, Constructive Approximation, 27:1 (2008), 1  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Yu. A. Farkov, M. E. Borisov, “Periodic dyadic wavelets and coding of fractal functions”, Russian Math. (Iz. VUZ), 56:9 (2012), 46–56  mathnet  crossref  mathscinet
    6. Prestin J. Schnieder J., “Polynomial Schauder Basis of Optimal Degree with Jacobi Orthogonality”, J. Approx. Theory, 174 (2013), 65–89  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. A. Yu. Trynin, “On necessary and sufficient conditions for convergence of sinc-approximations”, St. Petersburg Math. J., 27:5 (2016), 825–840  mathnet  crossref  mathscinet  isi  elib
    8. A. Yu. Trynin, “Approximation of continuous on a segment functions with the help of linear combinations of sincs”, Russian Math. (Iz. VUZ), 60:3 (2016), 63–71  mathnet  crossref  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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