Gaussian estimates for Schrödinger perturbations

Krzysztof Bogdan ¹   ; Karol Szczypkowski ²

¹ Institute of Mathematics Polish Academy of Sciences and Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
² Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Studia Mathematica, Tome 221 (2014) no. 2, pp. 151-173

Résumé

We propose a new general method of estimating Schrödinger perturbations of transition densities using an auxiliary transition density as a majorant of the perturbation series. We present applications to Gaussian bounds by proving an optimal inequality involving four Gaussian kernels, which we call the 4G Theorem. The applications come with honest control of constants in estimates of Schrödinger perturbations of Gaussian-type heat kernels and also allow for specific non-Kato perturbations.

Détail

DOI : 10.4064/sm221-2-4

Mots-clés : propose general method estimating schr dinger perturbations transition densities using auxiliary transition density majorant perturbation series present applications gaussian bounds proving optimal inequality involving gaussian kernels which call theorem applications come honest control constants estimates schr dinger perturbations gaussian type heat kernels allow specific non kato perturbations