Transmutation operators and a new representation for solutions of perturbed Bessel equations

DOI10.1002/mma.7189zbMath1478.34095arXiv2005.10403OpenAlexW3127061365MaRDI QIDQ5006994

Sergii M. Torba, Vladislav V. Kravchenko

Publication date: 18 August 2021

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.10403

zbMATH Keywords

Paley-Wiener theoremJacobi polynomialsSturm-Liouville theoryNeumann series of Bessel functionstransmutation operatorperturbed Bessel equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Theoretical approximation of solutions to ordinary differential equations (34A45) Sturm-Liouville theory (34B24) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Approximation by polynomials (41A10) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

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Transmutation operators and complete systems of solutions for the radial bicomplex Vekua equation ⋮ Theory of generalized Bessel potential space and functional completion ⋮ Professor Vladislav V. Kravchenko: a mathematician and a friend ⋮ Analytic approximation of transmutation operators for one-dimensional stationary Dirac operators and applications to solution of initial value and spectral problems ⋮ Inverse spectral problems for radial Schrödinger operators and closed systems

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