| Abstract: |
| Let $D$ be a bounded open subset of $\mathbb{R}^N$, and let $z_0 \in D$. Assume that the Newtonian potential of $D$ is proportional, outside $D$, to the potential generated by a point mass concentrated at $z_0$. Then $D$ is a Euclidean ball centred at $z_0$. This theorem, proved by Aharonov, Schiffer, and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this note, we extend the Suzuki--Watson theorem to a class of hypoelliptic Kolmogorov-type operators. |
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