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Matematicheskie Zametki, 2018, Volume 104, Issue 4, Pages 552–570
DOI: https://doi.org/10.4213/mzm12150 (Mi mzm12150) 		 
This article is cited in 16 scientific papers (total in 16 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
Full-text PDF (769 kB) Citations (16)
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DOI: https://doi.org/10.4213/mzm12150
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.
Received: 06.12.2017
English version:
Mathematical Notes, 2018, Volume 104, Issue 4, Pages 530–544
DOI: https://doi.org/10.1134/S0001434618090201
Bibliographic databases:
Document Type: Article
UDC: 517.912
Language: Russian
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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    • This publication is cited in the following 16 articles:
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