Heat content and small time asymptotics for Schrödinger operators on $R^d$

This paper studies the heat content} for Schrödinger operators of the fractional Laplacian $(-Δ)^{α/2}$, $0<α\leq 2$ 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, $α=2$.

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