Conservativeness of time changed processes and Liouville property for Schr\"odinger operators

Yuichi Shiozawa; Masayoshi Takeda

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arXiv · 2602.15411

Conservativeness of time changed processes and Liouville property for Schr\"odinger operators

Yuichi Shiozawa·Masayoshi Takeda

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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.

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Yuichi Shiozawa, Masayoshi Takeda. 2026-02-17. Conservativeness of time changed processes and Liouville property for Schr\"odinger operators. https://arxiv.org/abs/2602.15411

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