Heat content and small time asymptotics for Schrödinger operators on Rᵈ

Original · EN

This paper studies the heat content for Schrödinger operators of the fractional Laplacian (-Δ)α/², 0<α≤ 2 in Rᵈ, d≥ 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.