Heat content estimates for the fractional Schr\"odinger operator $\F+\ind$

TL;DR

This paper provides estimates for the heat content of the fractional Schrödinger operator with a potential, using analytic and probabilistic methods, applicable in higher-dimensional Lebesgue measure sets.

Contribution

It introduces new heat content estimates for the fractional Schrödinger operator with potential, extending previous results to more general sets and fractional orders.

Findings

Derived heat content estimates for the fractional Schrödinger operator.

Applied analytic and probabilistic techniques to obtain bounds.

Results are valid for sets with certain regularity in higher dimensions.

Abstract

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