PreprintCC BY-NC-ND 4.0arXiv
Liouville transforms for ordinary differential equations with distributional coefficients
Abstract
We study Liouville transforms for the differential equation Ju'+qu=wf on the real interval (a,b) where J is a constant, invertible, skew-hermitian matrix and q and w are matrices whose entries are distributions of order $0$ with q Hermitian and w non-negative. In particular, we examine their use in the treatment of quasi-regular endpoints and their impact on the Weyl-Titchmarsh 𝕄-function associated with the differential equation.
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BibTeX
@misc{weikard2026liouville,
title = {{Liouville transforms for ordinary differential equations with distributional coefficients}},
author = {Rudi Weikard},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08661},
eprint = {2611.08661},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08661},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Liouville transforms for ordinary differential equations with distributional coefficients
AU - Rudi Weikard
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08661
UR - https://arxiv.org/abs/2611.08661
AB - We study Liouville transforms for the differential equation Ju'+qu=wf on the real interval (a,b) where J is a constant, invertible, skew-hermitian matrix and q and w are matrices whose entries are distributions of order $0$ with q Hermitian and w non-negative. In particular, we examine their use in the treatment of quasi-regular endpoints and their impact on the Weyl-Titchmarsh 𝕄-function associated with the differential equation.
ER -