IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1103-d1077270.html
   My bibliography  Save this article

On Recovery of the Singular Differential Laplace—Bessel Operator from the Fourier–Bessel Transform

Author

Listed:
  • Sergey M. Sitnik

    (Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy St., 85, 308015 Belgorod, Russia)

  • Vladimir E. Fedorov

    (Department of Mathematical Analysis, Chelyabinsk State University, 129, Kashirin Brothers St., 454001 Chelyabinsk, Russia
    N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, 16, S.Kovalevskaya St., 620108 Yekaterinburg, Russia)

  • Marina V. Polovinkina

    (Department of Higher Mathematics and Information Technologies, Voronezh State University of Engineering Technologies, Revolution Av., 19, 394036 Voronezh, Russia)

  • Igor P. Polovinkin

    (Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy St., 85, 308015 Belgorod, Russia
    Department of Mathematical and Applied Analysis, Voronezh State University, Universitetskaya pl., 1, 394018 Voronezh, Russia)

Abstract

This paper is devoted to the problem of the best recovery of a fractional power of the B-elliptic operator of a function on R + N by its Fourier–Bessel transform known approximately on a convex set with the estimate of the difference between Fourier–Bessel transform of the function and its approximation in the metric L ∞ . The optimal recovery method has been found. This method does not use the Fourier–Bessel transform values beyond a ball centered at the origin.

Suggested Citation

  • Sergey M. Sitnik & Vladimir E. Fedorov & Marina V. Polovinkina & Igor P. Polovinkin, 2023. "On Recovery of the Singular Differential Laplace—Bessel Operator from the Fourier–Bessel Transform," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1103-:d:1077270
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1103/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1103/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1103-:d:1077270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.