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Mat. Tr., 2006, Volume 9, Number 1, Pages 52–100 (Mi mt39)  

This article is cited in 19 scientific papers (total in 19 papers)

Asymptotic Estimates for the Approximation and Entropy Numbers of a One-Weight Riemann–Liouville Operator

E. N. Lomakinaa, V. D. Stepanovb

a Computer Centre Far-Eastern Branch of RAS
b Peoples Friendship University of Russia

Abstract: We obtain two-sided estimates for the asymptotic behavior of the approximation and entropy numbers of a one-weight Riemann–Liouville operator of an arbitrary integer order acting in Lebesgue spaces on the semiaxis.

Key words: integral Riemann–Liouville operator, approximation and entropy numbers, Lebesgue space.

Full text: PDF file (2618 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2007, 17:1, 1–36

Bibliographic databases:

UDC: 517.98
Received: 12.07.2005

Citation: E. N. Lomakina, V. D. Stepanov, “Asymptotic Estimates for the Approximation and Entropy Numbers of a One-Weight Riemann–Liouville Operator”, Mat. Tr., 9:1 (2006), 52–100; Siberian Adv. Math., 17:1 (2007), 1–36

Citation in format AMSBIB
\Bibitem{LomSte06}
\by E.~N.~Lomakina, V.~D.~Stepanov
\paper Asymptotic Estimates for the~Approximation and Entropy Numbers of a~One-Weight Riemann--Liouville Operator
\jour Mat. Tr.
\yr 2006
\vol 9
\issue 1
\pages 52--100
\mathnet{http://mi.mathnet.ru/mt39}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2251331}
\transl
\jour Siberian Adv. Math.
\yr 2007
\vol 17
\issue 1
\pages 1--36
\crossref{https://doi.org/10.3103/S1055134407010014}


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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. A. A. Vasil'eva, “Kolmogorov Widths of Weighted Sobolev Classes on Closed Intervals”, Math. Notes, 84:5 (2008), 631–635  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Lomakina E.N., “Asymptotic estimates for approximation numbers of the Hardy operator in $Q$-Banach spaces”, Math. Inequal. Appl., 12:4 (2009), 815–825  mathscinet  zmath  isi  elib
    3. Stepanov V.D., Ushakova E.P., “Alternative criteria for the boundedness of Volterra integral operators in Lebesgue spaces”, Math. Inequal. Appl., 12:4 (2009), 873–889  mathscinet  zmath  isi  elib
    4. A. A. Vasil'eva, “Estimates for the widths of weighted Sobolev classes”, Sb. Math., 201:7 (2010), 947–984  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. A. Vasileva, “Kolmogorovskie poperechniki vesovykh klassov Soboleva na kube”, Tr. IMM UrO RAN, 16, no. 4, 2010, 100–116  mathnet  elib
    6. Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights. II”, Russ. J. Math. Phys., 18:4 (2011), 465–504  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights”, Russ. J. Math. Phys., 18:3 (2011), 353–385  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. A. A. Vasilyeva, “Kolmogorov widths and approximation numbers of Sobolev classes with singular weights”, St. Petersburg Math. J., 24:1 (2013), 1–27  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. A. Gogatishvili, V. D. Stepanov, “Reduction theorems for weighted integral inequalities on the cone of monotone functions”, Russian Math. Surveys, 68:4 (2013), 597–664  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. E. P. Ushakova, “Upper estimates for the approximation numbers of the generalized Laplace transform”, Proc. Steklov Inst. Math., 283 (2013), 260–280  mathnet  crossref  crossref  mathscinet  isi  elib
    11. Vasil'eva A.A., “Widths of Weighted Sobolev Classes on a John Domain: Strong Singularity at a Point”, Rev. Mat. Complut., 27:1 (2014), 167–212  crossref  mathscinet  zmath  isi  scopus
    12. Carl B., Hinrichs A., Rudolph Ph., “Entropy Numbers of Convex Hulls in Banach Spaces and Applications”, J. Complex., 30:5 (2014), 555–587  crossref  mathscinet  zmath  isi  elib  scopus
    13. Lifshits M., Linde W., “Fractional Integration Operators of Variable Order: Continuity and Compactness Properties”, Math. Nachr., 287:8-9 (2014), 980–1000  crossref  mathscinet  zmath  isi  elib  scopus
    14. A. A. Vasil'eva, “Estimates for the widths of discrete function classes generated by a two-weight summation operator”, Proc. Steklov Inst. Math., 294 (2016), 291–307  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    15. Vasil'eva A.A., “Estimates For the Entropy Numbers of Embedding Operators of Function Spaces on Sets With Tree-Like Structure: Some Limiting Cases”, J. Complex., 36 (2016), 74–105  crossref  mathscinet  zmath  isi  scopus
    16. A. A. Vasil'eva, “Entropy numbers of embedding operators of function spaces on sets with tree-like structure”, Izv. Math., 81:6 (2017), 1095–1142  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. Nasyrova M.G., Ushakova E.P., “Wavelet Bases and Entropy Numbers of Hardy Operator”, Anal. Math., 44:4 (2018), 543–576  crossref  mathscinet  zmath  isi  scopus
    18. A. A. Vasil'eva, “Kolmogorov Widths of Weighted Sobolev Classes on an Interval with Conditions on the Zeroth and First Derivatives”, Math. Notes, 107:3 (2020), 522–524  mathnet  crossref  crossref  mathscinet  isi  elib
    19. A. A. Vasil'eva, “Kolmogorov widths of intersections of weighted Sobolev classes on an interval with conditions on the zeroth and first derivatives”, Izv. Math., 85:1 (2021), 1–23  mathnet  crossref  crossref  mathscinet  isi
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