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Tr. Mat. Inst. Steklova, 1997, Volume 219, Pages 269–285 (Mi tm620)  

This article is cited in 18 scientific papers (total in 18 papers)

Ridge Approximation, Chebyshev–Fourier Analysis and Optimal Quadrature Formulas

K. I. Oskolkov


Full text: PDF file (1692 kB)

English version:
Proceedings of the Steklov Institute of Mathematics, 1997, 219, 265–280

Bibliographic databases:
UDC: 517.518
Received in June 1997

Citation: K. I. Oskolkov, “Ridge Approximation, Chebyshev–Fourier Analysis and Optimal Quadrature Formulas”, Approximation theory. Harmonic analysis, Collection of papers dedicated to the memory of Professor Sergei Borisovich Stechkin, Tr. Mat. Inst. Steklova, 219, Nauka, MAIK Nauka, M., 1997, 269–285; Proc. Steklov Inst. Math., 219 (1997), 265–280

Citation in format AMSBIB
\Bibitem{Osk97}
\by K.~I.~Oskolkov
\paper Ridge Approximation, Chebyshev--Fourier Analysis and Optimal Quadrature Formulas
\inbook Approximation theory. Harmonic analysis
\bookinfo Collection of papers dedicated to the memory of Professor Sergei Borisovich Stechkin
\serial Tr. Mat. Inst. Steklova
\yr 1997
\vol 219
\pages 269--285
\publ Nauka, MAIK Nauka
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm620}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1642280}
\zmath{https://zbmath.org/?q=an:0936.41013}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1997
\vol 219
\pages 265--280


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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. Maiorov V.E., “On best approximation by ridge functions”, Journal of Approximation Theory, 99:1 (1999), 68–94  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Maiorov V., Meir R., Ratsaby J., “On the approximation of functional classes equipped with a uniform measure using ridge functions”, Journal of Approximation Theory, 99:1 (1999), 95–111  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Oskolkov K., “Ridge Approximation and Kolmogorov-Nikol'Skii Problem”, Dokl. Akad. Nauk, 368:4 (1999), 445–448  mathnet  mathscinet  zmath  isi
    4. Gordon Y., Maiorov V., Meyer M., Reisner S., “On the best approximation by ridge functions in the uniform norm”, Constructive Approximation, 18:1 (2002), 61–85  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Maiorov V., “On best approximation of classes by radial functions”, Journal of Approximation Theory, 120:1 (2003), 36–70  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Temlyakov V.N., “Nonlinear methods of approximation”, Foundations of Computational Mathematics, 3:1 (2003), 33–107  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Hemmat A.A., Dehghan M.A., Skopina M., “Ridge wavelets on the ball”, Journal of Approximation Theory, 136:2 (2005), 129–139  crossref  mathscinet  zmath  isi  scopus  scopus
    8. K. I. Oskolkov, “Linear and Nonlinear Methods of Relief Approximation”, Journal of Mathematical Sciences, 155:1 (2008), 129–152  mathnet  crossref  mathscinet  zmath
    9. Ismailov V.E., “On the approximation by compositions of fixed multivariate functions with univariate functions”, Studia Mathematica, 183:2 (2007), 117–126  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Konovalov V.N., Leviatan D., Maiorov V.E., “Approximation by polynomials and ridge functions of classes of s–monotone radial functions”, Journal of Approximation Theory, 152:1 (2008), 20–51  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Ismailov V.E., “On the representation by linear superpositions”, Journal of Approximation Theory, 151:2 (2008), 113–125  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Konovalov V.N., Leviatan D., Maiorov V.E., “Approximation of Sobolev classes by polynomials and ridge functions”, Journal of Approximation Theory, 159:1 (2009), 97–108  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Maiorov V., “Geometric properties of the ridge function manifold”, Advances in Computational Mathematics, 32:2 (2010), 239–253  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Maiorov V.E., “Best Approximation by Ridge Functions in l (P)-Spaces”, Ukrainian Math J, 62:3 (2010), 452–466  crossref  zmath  isi  scopus  scopus
    15. Konovalov V.N., Kopotun K.A., Maiorov V.E., “Convex Polynomial and Ridge Approximation of Lipschitz Functions in R-d”, Rocky Mountain J Math, 40:3 (2010), 957–976  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    16. V. E. Ismailov, “Approximation by sums of ridge functions with fixed directions”, St. Petersburg Math. J., 28:6 (2017), 741–772  mathnet  crossref  isi  elib
    17. Sun X., Liang X., “Fast and Exact 2D Image Reconstruction Based on Hakopian Interpolation”, Appl. Numer. Math., 121 (2017), 185–197  crossref  mathscinet  zmath  isi  scopus  scopus
    18. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some problems in the theory of ridge functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169  mathnet  crossref  crossref  isi  elib  elib
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