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 Mat. Sb., 1992, Volume 183, Number 2, Pages 3–20 (Mi msb1466)

Some problems in approximation theory for a class of functions of finite smoothness

S. N. Kudryavtsev

Abstract: This paper concerns the problem of best accuracy in recovering functions from their values at a specified number of points, the problem of best approximation of partial differential operators by bounded operators, and the problem of the accuracy of approximation of one class by another for a class of functions with partial derivatives of a fixed order having moduli of continuity not exceeding a given modulus of continuity. The weak asymptotic behavior is established for the corresponding quantities.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:1, 145–164

Bibliographic databases:

MSC: Primary 41A65, 41A46; Secondary 41A35

Citation: S. N. Kudryavtsev, “Some problems in approximation theory for a class of functions of finite smoothness”, Mat. Sb., 183:2 (1992), 3–20; Russian Acad. Sci. Sb. Math., 75:1 (1993), 145–164

Citation in format AMSBIB
\Bibitem{Kud92} \by S.~N.~Kudryavtsev \paper Some problems in approximation theory for a~class of functions of finite smoothness \jour Mat. Sb. \yr 1992 \vol 183 \issue 2 \pages 3--20 \mathnet{http://mi.mathnet.ru/msb1466} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1166949} \zmath{https://zbmath.org/?q=an:0774.41019|0766.41018} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..75..145K} \transl \jour Russian Acad. Sci. Sb. Math. \yr 1993 \vol 75 \issue 1 \pages 145--164 \crossref{https://doi.org/10.1070/SM1993v075n01ABEH003377} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LG75100009} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. N. Kudryavtsev, “Recovering a function with its derivatives from function values at a given number of points”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 505–528
2. S. N. Kudryavtsev, “Approximation of a partial differential operator by bounded operators on a class of functions of finite smoothness”, Sb. Math., 187:3 (1996), 385–402
3. S. N. Kudryavtsev, “Approximating one class of finitely differentiable functions by another”, Izv. Math., 61:2 (1997), 347–362
4. S. N. Kudryavtsev, “The best accuracy of reconstruction of finitely smooth functions from their values at a given number of points”, Izv. Math., 62:1 (1998), 19–53
5. S. N. Kudryavtsev, “The Stechkin problem for partial derivation operators on classes of finitely smooth functions”, Math. Notes, 67:1 (2000), 61–68
6. Proc. Steklov Inst. Math., 248 (2005), 268–277
7. Sh. U. Azhgaliev, N. Temirgaliev, “Informativeness of all the linear functionals in the recovery of functions in the classes $H_p^\omega$”, Sb. Math., 198:11 (2007), 1535–1551
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