Heat content estimates for the fractional Schrödinger operator $\F+\ind$

Abstract

This paper establishes by employing analytic and probabilistic techniques estimates concerning the {\it heat content} for the fractional Schrödinger operator $\F+\ind$ with $0<\alpha \le 2$ in $\Rd$, $d\ge 2$ and $\dom$ a Lebesgue measure set satisfying some regularity conditions.