English

Spectral upper bound for the torsion function of symmetric stable processes

Probability 2021-10-19 v3 Mathematical Physics Analysis of PDEs math.MP Spectral Theory

Abstract

We prove a spectral upper bound for the torsion function of symmetric stable processes that holds for convex domains in Rd\mathbb{R}^d. Our bound is explicit and captures the correct order of growth in dd, improving upon the existing results of Giorgi and Smits (2010) and Biswas and L\H{o}rinczi (2019). Along the way, we make progress towards a torsion analogue of Chen and Song's (2005) two-sided eigenvalue estimates for subordinate Brownian motion.

Keywords

Cite

@article{arxiv.2001.04972,
  title  = {Spectral upper bound for the torsion function of symmetric stable processes},
  author = {Hugo Panzo},
  journal= {arXiv preprint arXiv:2001.04972},
  year   = {2021}
}

Comments

15 pages, 1 figure, to appear in Proceedings of the American Mathematical Society

R2 v1 2026-06-23T13:11:12.888Z