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A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications

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  • Khmelnytskaya, Kira V.
  • Kravchenko, Vladislav V.
  • Torba, Sergii M.

Abstract

The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schrödinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding Sturm–Liouville problem. Since both series converge slowly and in general only in a certain distributional sense we find a way to improve these expansions and make them convergent uniformly and absolutely by adding and subtracting corresponding terms. A numerical illustration of the obtained results is given.

Suggested Citation

  • Khmelnytskaya, Kira V. & Kravchenko, Vladislav V. & Torba, Sergii M., 2019. "A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 274-281.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:274-281
    DOI: 10.1016/j.amc.2019.02.024
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    References listed on IDEAS

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    1. Kravchenko, Vladislav V., 2018. "Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 75-81.
    2. Kravchenko, Vladislav V. & Navarro, Luis J. & Torba, Sergii M., 2017. "Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 173-192.
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