Conservativeness of time changed processes and Liouville property for Schr\"odinger operators
Probability
2026-02-18 v1
Abstract
We establish a criterion for the Liouville property for Schr\"odinger operators via the conservativeness of time changed processes. Using this criterion, we obtain necessary and sufficient conditions for the Liouville property for some Schr\"odinger operators in terms of the decay rates of the potentials at infinity/boundary.
Keywords
Cite
@article{arxiv.2602.15411,
title = {Conservativeness of time changed processes and Liouville property for Schr\"odinger operators},
author = {Yuichi Shiozawa and Masayoshi Takeda},
journal= {arXiv preprint arXiv:2602.15411},
year = {2026}
}