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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 1, Pages 177–198 (Mi izv110)  

This article is cited in 4 scientific papers (total in 5 papers)

Extremal $L_p$ interpolation in the mean with intersecting averaging intervals

Yu. N. Subbotin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We find the smallest constant $A=A(n,p,h)$ ($1<h<2$, $1<p<\infty$) such that for any sequence $y_k$, $k\in\mathbb Z$ whose $n$th differences are bounded by one in $l_p$ there is a function $f(x)$ with locally absolutely continuous $(n-1)$th derivative and with $n$th derivative in $L_p(\mathbb R)$ not exceeding $A$ that satisfies the mean interpolation conditions $\frac{1}{h} \int _{-h/2}^{h/2}f(k+t) dt=y_k$ ($k\in\mathbb Z$). Until now the solution to this problem was known only for non-intersecting averaging intervals ($0\geqslant h\geqslant 1$).

DOI: https://doi.org/10.4213/im110

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English version:
Izvestiya: Mathematics, 1997, 61:1, 183–205

Bibliographic databases:

MSC: 41A05
Received: 12.01.1995

Citation: Yu. N. Subbotin, “Extremal $L_p$ interpolation in the mean with intersecting averaging intervals”, Izv. RAN. Ser. Mat., 61:1 (1997), 177–198; Izv. Math., 61:1 (1997), 183–205

Citation in format AMSBIB
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\by Yu.~N.~Subbotin
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\pages 183--205
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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. V. T. Shevaldin, “Extremal interpolation in the mean with overlapping averaging intervals and $L$-splines”, Izv. Math., 62:4 (1998), 833–856  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. E. V. Shevaldina, “Approksimatsiya lokalnymi parabolicheskimi splainami funktsii po ikh znacheniyam v srednem”, Tr. IMM UrO RAN, 13, no. 4, 2007, 169–189  mathnet  elib
    3. “Yurii Nikolaevich Subbotin. (K semidesyatipyatiletiyu so dnya rozhdeniya)”, Tr. IMM UrO RAN, 17, no. 3, 2011, 8–13  mathnet
    4. Elena V. Strelkova, “Approximation by local parabolic splines constructed on the basis of interpolationin the mean”, Ural Math. J., 3:1 (2017), 81–94  mathnet  crossref
    5. Yu. N. Subbotin, S. I. Novikov, V. T. Shevaldin, “Ekstremalnaya funktsionalnaya interpolyatsiya i splainy”, Tr. IMM UrO RAN, 24, no. 3, 2018, 200–225  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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