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

preprint2021arXivOpen access

Abstract

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 αis in (1, 2) or α= 1. We prove that in the 3rd term of spectral heat content, one can observe the length b-a of the interval D.

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