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Mat. Zametki, 2018, Volume 104, Issue 4, Pages 552–570 (Mi mz12150)  

This article is cited in 2 scientific papers (total in 2 papers)

On a Series Representation for Integral Kernels of Transmutation Operators for Perturbed Bessel Equations

V. V. Kravchenkoab, E. L. Shishkinac, S. M. Torbaa

a CINVESTAV del IPN
b Southern Federal University
c Voronezh State University

Abstract: A representation for the kernel of the transmutation operator relating a perturbed Bessel equation to the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties of the transmutation kernel are established. A new representation of a regular solution of a perturbed Bessel equation is given, which admits a uniform error bound with respect to the spectral parameter for partial sums of the series. A numerical illustration of the application of the obtained result to solve Dirichlet spectral problems is presented.

Keywords: perturbed Bessel equation, transmutation operators, Neumann series of Bessel functions, Erdelyi–Kober operators, Jacobi polynomials, spectral problems.

Funding Agency Grant Number
CONACYT - Consejo Nacional de Ciencia y Tecnología 222478
284470
This work was supported by CONACYT, Mexico, via grant no. 222478 and 284470.


DOI: https://doi.org/10.4213/mzm12150

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English version:
Mathematical Notes, 2018, 104:4, 530–544

Bibliographic databases:

UDC: 517.912
Received: 06.12.2017

Citation: V. V. Kravchenko, E. L. Shishkina, S. M. Torba, “On a Series Representation for Integral Kernels of Transmutation Operators for Perturbed Bessel Equations”, Mat. Zametki, 104:4 (2018), 552–570; Math. Notes, 104:4 (2018), 530–544

Citation in format AMSBIB
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\jour Mat. Zametki
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Khmelnytskaya V K., Kraychenko V.V., Torba S.M., “A Representation of the Transmutation Kernels For the Schrodinger Operator in Terms of Eigenfunctions and Applications”, Appl. Math. Comput., 353 (2019), 274–281  crossref  mathscinet  isi  scopus
    2. E. L. Shishkina, “Obschee uravnenie Eilera—Puassona—Darbu i giperbolicheskie $B$-potentsialy”, Uravneniya v chastnykh proizvodnykh, SMFN, 65, no. 2, Rossiiskii universitet druzhby narodov, M., 2019, 157–338  mathnet  crossref
  • Математические заметки Mathematical Notes
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