Gaussian estimates for Schrödinger perturbations

• Autorzy: Krzysztof Bogdan , Karol Szczypkowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47D08: Schr\"odinger and Feynman-Kac semigroups
• 47D06: One-parameter semigroups and linear evolution equations
• 35A08: Fundamental solutions
• 35B25: Singular perturbations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 2
• Strony: 151-173

Daty

wydano

2014

Twórcy

autor

Krzysztof Bogdan

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

autor

Karol Szczypkowski

• Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm221-2-4