Invariance of intrinsic hypercontractivity under perturbation of Schr\'odinger operators

Autor:	Gross, Leonard
Rok vydání:	2024
Předmět:	Mathematical Physics Mathematics - Functional Analysis 81Q15 47D08 (Primary) 35J10 35B20 60J46 (Secondary)
Druh dokumentu:	Working Paper
Popis:	A Schr\"odinger operator that is bounded below and has a unique positive ground state can be transformed into a Dirichlet form operator by the ground state transformation. If the resulting Dirichlet form operator is hypercontractive, Davies and Simon call the Schr\"odinger operator ``intrinsically hypercontractive". I will show that if one adds a suitable potential onto an intrinsically hypercontractive Schr\"odinger operator it remains intrinsically hypercontractive. The proof uses a fortuitous relation between the WKB equation and logarithmic Sobolev inequalities. All bounds are dimension independent. The main theorem will be applied to several examples. Comment: 123 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.20282 Zobrazit plný text záznamu View this record from Arxiv