PreprintarXiv licencearXiv
Transmutation operators for the Sturm--Liouville equation in impedance form with an integrable potential
Abstract
In this work, we study a family of transmutation operators for the Sturm--Liouville operator in impedance form with an integrable potential satisfying a smallness condition. Specifically, we consider transmutations associated with the pair Lr=1/(r2 (x))d/dxr2 (x)d/dx and M=d2/dx2. We extend existing results by showing that a particular transmutation operator on W3,1 (−a,a) can be represented in integral form, where the kernel function satisfies a corresponding Goursat problem. We establish the existence of this kernel using two distinct approaches: the classical method of successive approximations and an application of Picard's theorem.
Related
- Analytic Liouville Integrable Geodesic Flow Has Zero Entropy
- A Twisted Affine Interpolation of the ℤ22-graded Integrable Super-Liouville and super-Sinh-Gordon Equations
- L-tauberian operators and subspaces with equi-integrable unit ball
- The spectral ζ-function of Sturm--Liouville operators with N generalized point potentials
- Lp-Liouville properties and realizations of Schrödinger operators on incomplete Riemannian manifolds
BibTeX
@misc{delgado2026transmutation,
title = {{Transmutation operators for the Sturm--Liouville equation in impedance form with an integrable potential}},
author = {Briceyda B. Delgado and F. Ayça Çetinkaya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28772},
eprint = {2609.28772},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28772},
}
RIS
TY - UNPB
TI - Transmutation operators for the Sturm--Liouville equation in impedance form with an integrable potential
AU - Briceyda B. Delgado
AU - F. Ayça Çetinkaya
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28772
UR - https://arxiv.org/abs/2609.28772
AB - In this work, we study a family of transmutation operators for the Sturm--Liouville operator in impedance form with an integrable potential satisfying a smallness condition. Specifically, we consider transmutations associated with the pair L_r=1/(r^2 (x))d/dxr^2 (x)d/dx and M=d^2/dx^2. We extend existing results by showing that a particular transmutation operator on W^3,1 (−a,a) can be represented in integral form, where the kernel function satisfies a corresponding Goursat problem. We establish the existence of this kernel using two distinct approaches: the classical method of successive approximations and an application of Picard's theorem.
ER -