Higher order terms of spectral heat content for killed subordinate and subordinate killed Brownian motions related to symmetric α-stable processes in R

Hyunchul Park

Published 2020-05-26Version 1

We investigate the 3rd term of spectral heat content for killed subordinate and subordinate killed Brownian motions on a bounded open interval D = (a, b) in a real line when the underlying subordinators are stable subordinators with index \alpha is in (1, 2) or \alpha = 1. We prove that in the 3rd term of spectral heat content, one can observe the length b-a of the interval D.