Spectral Asymptotics for Fractional Laplacians

TL;DR

This paper investigates the spectral asymptotics of fractional Laplacians, a class of operators relevant to probability theory, and derives a two-term asymptotic expansion using adapted methods.

Contribution

It introduces a novel approach to obtain two-term spectral asymptotics for fractional Laplacians, extending existing techniques to this new class of operators.

Findings

Derived two-term spectral asymptotics for fractional Laplacians

Extended classical methods to fractional operators

Provided insights relevant to probability theory

Abstract

In this article we consider fractional Laplacians which seem to be of interest to probability theory. This is a rather new class of operators for us but our methods works (with a twist, as usual). Our main goal is to derive a two-term asymptotics as one-term asymptotics is easily obtained by R.~Seeley's method.