English

Generalized wave polynomials and transmutations related to perturbed Bessel equations

Classical Analysis and ODEs 2018-03-26 v2 Analysis of PDEs Numerical Analysis

Abstract

The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave polynomials, solutions of a singular hyperbolic partial differential equation arising in relation with the transmutation kernel. As a corollary of this results an approximation of the regular solution of the perturbed Bessel equation is proposed with corresponding estimates independent of the spectral parameter.

Keywords

Cite

@article{arxiv.1606.07850,
  title  = {Generalized wave polynomials and transmutations related to perturbed Bessel equations},
  author = {Vladislav V. Kravchenko and Sergii M. Torba and Jessica Yu. Santana-Bejarano},
  journal= {arXiv preprint arXiv:1606.07850},
  year   = {2018}
}

Comments

25 pages, corrected proof of Lemma A.2

R2 v1 2026-06-22T14:33:59.891Z