Generalized wave polynomials and transmutations related to perturbed Bessel equations
Provides a theoretical approximation tool for perturbed Bessel equations, but the results are purely analytical with no demonstrated application or numerical validation.
The paper constructs generalized wave polynomials to uniformly approximate the integral kernel of the transmutation operator for perturbed Bessel equations, enabling spectral-parameter-independent approximation of regular solutions.
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.