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arXiv · 1401.2971

Heat content and small time asymptotics for Schr\"odinger operators on $R^d$

Luis Acuña Valverde·Rodrigo Bañuelos
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Abstract

This paper studies the heat content} for Schr\"odinger operators of the fractional Laplacian $(-\Delta)^{\alpha/2}$, $0<\alpha\leq 2$ in $R^d$, $d\geq 1$. Employing probabilistic and analytic techniques, a small time asymptotic expansion formula is given and the "heat content invariants" are identified. These results are new even in the case of the Laplacian, $\alpha=2$.

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Luis Acuña Valverde, Rodrigo Bañuelos. 2014-01-13. Heat content and small time asymptotics for Schr\"odinger operators on $R^d$. https://arxiv.org/abs/1401.2971

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