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Matematicheskie Trudy, 2015, Volume 18, Number 2, Pages 22–38
DOI: https://doi.org/10.17377/mattrudy.2015.18.202 (Mi mt291) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On partial derivatives of multivariate Bernstein polynomials

A. Yu. Veretennikovabc, E. V. Veretennikovad

a Institute for Information Transmission Problems, Russian Academy of Sciences
b University of Leeds
c National Research University "Higher School of Economics" (HSE), Moscow
d Moscow Pedagogical University, Moscow, Russian Federation, Moscow
Full-text PDF (231 kB) Citations (9)
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DOI: https://doi.org/10.17377/mattrudy.2015.18.202
Abstract: It is shown that Bernstein polynomials for a multivariate function converge to this function along with partial derivatives provided that the latter derivatives exist and are continuous. This result may be useful in some issues of stochastic calculus.
Key words: multivariate Bernstein polynomial, partial derivative, convergence.
Funding agency Grant number
National Research University Higher School of Economics
Received: 10.10.2014
English version:
Siberian Advances in Mathematics, 2016, Volume 26, Issue 4, Pages 294–305
DOI: https://doi.org/10.3103/S1055134416040039
Bibliographic databases:
Document Type: Article
UDC: 519.21:519.65:517.518.8
Language: Russian
Citation: A. Yu. Veretennikov, E. V. Veretennikova, “On partial derivatives of multivariate Bernstein polynomials”, Mat. Tr., 18:2 (2015), 22–38; Siberian Adv. Math., 26:4 (2016), 294–305
Citation in format AMSBIB
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\by A.~Yu.~Veretennikov, E.~V.~Veretennikova
\paper On partial derivatives of multivariate Bernstein polynomials
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\vol 18
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\pages 22--38
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\crossref{https://doi.org/10.17377/mattrudy.2015.18.202}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588289}
\elib{https://elibrary.ru/item.asp?id=24639777}
\transl
\jour Siberian Adv. Math.
\yr 2016
\vol 26
\issue 4
\pages 294--305
\crossref{https://doi.org/10.3103/S1055134416040039}
Linking options:
  • https://www.mathnet.ru/eng/mt291
  • https://www.mathnet.ru/eng/mt/v18/i2/p22
    • This publication is cited in the following 9 articles:
    1. Vitalii Konarovskyi, Max-K. von Renesse, “Reversible coalescing-fragmentating Wasserstein dynamics on the real line”, Journal of Functional Analysis, 286:8 (2024), 110342  crossref
    2. Paul Ressel, “Functions operating on several multivariate distribution functions”, Dependence Modeling, 11:1 (2023)  crossref
    3. Lucas L. Fernandes, Morgan Jones, Luis Alberto, Matthew Peet, Daniel Dotta, “Combining Trajectory Data With Analytical Lyapunov Functions for Improved Region of Attraction Estimation”, IEEE Control Syst. Lett., 7 (2023), 271  crossref
    4. Randy A. Freeman, Lecture Notes in Control and Information Sciences, 488, Trends in Nonlinear and Adaptive Control, 2022, 43  crossref
    5. V. Konarovskyi, T. Lehmann, M. von Renesse, “On Dean-kawasaki dynamics with smooth drift potential”, J. Stat. Phys., 178:3 (2020), 666–681  crossref  mathscinet  zmath  isi  scopus
    6. Mama Foupouagnigni, Merlin Mouafo Wouodjié, “On Multivariate Bernstein Polynomials”, Mathematics, 8:9 (2020), 1397  crossref
    7. Amir Ali Ahmadi, Bachir El Khadir, “On Algebraic Proofs of Stability for Homogeneous Vector Fields”, IEEE Trans. Automat. Contr., 65:1 (2020), 325  crossref
    8. Chunxi Jiao, Reiichiro Kawai, “Computable Primal and Dual Bounds for Stochastic Control”, SIAM J. Control Optim., 58:6 (2020), 3709  crossref
    9. A. S. Shvedov, “Approksimatsiya funktsii s pomoschyu neironnykh setei i nechetkikh sistem”, Probl. upravl., 1 (2018), 21–29  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические труды Siberian Advances in Mathematics
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