Spectral heat content for Lévy processes

Tomasz Grzywny, Hyunchul Park, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the spectral heat content for various Lévy processes. We establish the small time asymptotic behavior of the spectral heat content for Lévy processes of bounded variation in ℝ , 푑 ≥ 1. We also study the spectral heat content for arbitrary open sets of finite Lebesgue measure in R with respect to symmetric Lévy processes of unbounded variation under certain conditions on their characteristic exponents. Finally, we establish that the small time asymptotic behavior of the spectral heat content is stable under integrable perturbations to the Lévy measure.

Original languageEnglish (US)
Pages (from-to)805-825
Number of pages21
JournalMathematische Nachrichten
Volume292
Issue number4
DOIs
StatePublished - Apr 2019

Keywords

  • Lévy process
  • heat content
  • infinitesimal generator
  • spectral heat content

ASJC Scopus subject areas

  • Mathematics(all)

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