A+ CATEGORY SCIENTIFIC UNIT

Gaussian estimates for Schrödinger perturbations

Volume 221 / 2014

Krzysztof Bogdan, Karol Szczypkowski Studia Mathematica 221 (2014), 151-173 MSC: Primary 47D06, 47D08; Secondary 35A08, 35B25. DOI: 10.4064/sm221-2-4

Abstract

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.

Authors

  • Krzysztof BogdanInstitute of Mathematics
    Polish Academy of Sciences
    and
    Institute of Mathematics
    and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Karol SzczypkowskiInstitute of Mathematics
    and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image