Invariance of intrinsic hypercontractivity under perturbation of Schrödinger operators

2024/12/28 by Leonard Gross, Gross, Leonard · 1 voice · 3 citations
Mathematics · #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.20282

Abstract

A Schrödinger 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 Schrödinger operator ``intrinsically hypercontractive". I will show that if one adds a suitable potential onto an intrinsically hypercontractive Schrödinger 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.

Cited by

• Infinite-dimensional nonlinear stationary Fokker-Planck-Kolmogorov equations
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Discussions

• Many cool things up this morning: arxiv.org/abs/2412.20282 'Invariance of intrinsic hypercontractivity under perturbation of Schrödinger operators' - Leonard Gross [bsky, 10 points, 1 comments]

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