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Mat. Zametki, 2008, Volume 84, Issue 1, Pages 59–68 (Mi mz3865)  

This article is cited in 6 scientific papers (total in 6 papers)

Exact Lebesgue Constants for Interpolatory $\mathscr L$-Splines of Third Order

V. A. Kim

Ural State University

Abstract: In this paper, we obtain the Lebesgue constants for interpolatory $\mathscr L$-splines of third order with uniform nodes, i.e., the norms of interpolation operators from $\mathrm C$ to $\mathrm C$ describing the process of interpolation of continuous bounded and continuous periodic functions by $\mathscr L$-splines of third order with uniform nodes on the real line. As a corollary, we obtain exact Lebesgue constants for interpolatory polynomial parabolic splines with uniform nodes.

Keywords: Lebesgue constant, interpolatory $\mathscr L$-spline, $B$-spline, polynomial parabolic spline with uniform nodes, continuous bounded function, continuous periodic function

DOI: https://doi.org/10.4213/mzm3865

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English version:
Mathematical Notes, 2008, 84:1, 55–63

Bibliographic databases:

UDC: 517.518.8
Received: 26.03.2007

Citation: V. A. Kim, “Exact Lebesgue Constants for Interpolatory $\mathscr L$-Splines of Third Order”, Mat. Zametki, 84:1 (2008), 59–68; Math. Notes, 84:1 (2008), 55–63

Citation in format AMSBIB
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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. A. Kim, “Sharp Lebesgue constants for bounded cubic interpolation $\mathcal L$-splines”, Siberian Math. J., 51:2 (2010), 267–276  mathnet  crossref  mathscinet  isi  elib  elib
    2. V. A. Kim, “Tochnye konstanty Lebega dlya interpolyatsionnykh $\mathcal L$-splainov formalno samosopryazhennogo differentsialnogo operatora”, Tr. IMM UrO RAN, 17, no. 3, 2011, 169–177  mathnet  elib
    3. E. V. Strelkova, V. T. Shevaldin, “On Lebesgue constants of local parabolic splines”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 192–198  mathnet  crossref  mathscinet  isi  elib
    4. E. V. Strelkova, V. T. Shevaldin, “On uniform Lebesgue constants of local exponential splines with equidistant knots”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 206–217  mathnet  crossref  mathscinet  elib
    5. E. V. Strelkova, V. T. Shevaldin, “O ravnomernykh konstantakh Lebega lokalnykh trigonometricheskikh splainov tretego poryadka”, Tr. IMM UrO RAN, 22, no. 2, 2016, 245–254  mathnet  crossref  mathscinet  elib
    6. S. I. Novikov, “Lebesgue constants for some interpolational ${\mathcal L}$-splines”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 136–144  mathnet  crossref  crossref  mathscinet  isi  elib
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