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

Abstract

This paper studies the heat content} for Schrödinger operators of the fractional Laplacian $(-\Delta {)}^{\alpha /2}$, $0<\alpha \le 2$ in $R^d$, $d\ge 1$. 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, $\alpha =2$.

References in corpus (2)

• Lieb-Thirring Bound for Schrödinger Operators with Bernstein Functions of the Laplacian
• Heat Trace of non-local operators

Cited by in corpus (2)

• Heat content for stable processes in domains of ${\mathbb{R}}^d$
• Heat content estimates over sets of finite perimeter