Generalized wave polynomials and transmutations related to perturbed Bessel equations. (2nd August 2018)

• Record Type: Journal Article
• Authors: Kravchenko, Vladislav V.; Torba, Sergii M.; Santana‐Bejarano, Jessica Yu.
• Other Names: Kravchenko Vladislav V. guestEditor.; Porter R. Michael guestEditor.; Torba Sergii M. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 15(2019)
• Page Start: 5008
• Page End: 5028
• Publication Date: 2018-08-02
• Subjects: complete system of solutions -- Perturbed Bessel equation -- Riemann function -- singular hyperbolic equation -- Sturm‐Liouville problems -- transmutation operators; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5195
• Languages: English
• ISSNs: 0170-4214

Abstract

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 result an approximation of the regular solution of the perturbed Bessel equation is proposed with corresponding estimates independent of the spectral parameter.