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arXiv · 2310.20541

Observability and unique continuation inequalities for the Schrödinger equations with inverse-square potentials

Hui Xu·Longben Wei·Zhiwen Duan
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Abstract

This paper is inspired by Wang, Wang and Zhang's work [ Observability and unique continuation inequalities for the Schrödinger equation. J. Eur. Math. Soc. 21, 3513--3572 (2019)], where they present several observability and unique continuation inequalities for the free Schrödinger equation in $\mathbb{R}^{n}$. We extend all such observability and unique continuation inequalities for the Schrödinger equations on half-line with inverse-square potentials. Technically, the proofs essentially rely on the representation of the solution, a Nazarov type uncertainty principle for the Hankel transform and an interpolation inequality for functions whose Hankel transform have compact support.

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Hui Xu, Longben Wei, Zhiwen Duan. 2023-10-31. Observability and unique continuation inequalities for the Schrödinger equations with inverse-square potentials. https://arxiv.org/abs/2310.20541

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