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Estimates of Schrödinger perturbation series

Le : 13/01/2014 11h00
Par : Karol SZCZYPKOWSKI (E.Polytechnique de Wroclaw )
Lieu : I103
Lien web :
Résumé : A perturbation series is an explicit method of constructing new semigroups or fundamental solutions. It is thus of the interest to obtain its upper and lower bounds. We propose a new general method of estimating Schröodinger 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 4G Theorem for the Gaussian kernel, the inequality which is a non-trivial extension of the so called 3G or 3P Theorem (as well known, 3P fails in its primary form for the Gaussian kernel). Further applications concern transition denisty of 1/2 stable subordinator. The talk is based on the paper [1] and other recent results. References [1] K. Bogdan and K. Szczypkowski. Gaussian estimates for Schrödinger perturbations. submitted.