Time-dependent Schrödinger perturbations of transition densities

• Autorzy: Krzysztof Bogdan , Wolfhard Hansen , Tomasz Jakubowski
• Języki publikacji: EN

Abstrakty

EN

We construct the fundamental solution of $∂_t - Δ_y - q(t,y)$ for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the relative Kato condition.
The result is generalized to arbitrary strictly positive and finite time-nonhomogeneous transition densities on measure spaces.
We also discuss specific applications to Schrödinger perturbations of the fractional Laplacian in view of the fact that the 3P Theorem holds for the fundamental solution corresponding to the operator.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 47A55: Perturbation theory
• 60J57: Multiplicative functionals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 189
• Numer: 3
• Strony: 235-254

Daty

wydano

2008

Twórcy

autor

Krzysztof Bogdan

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

autor

Wolfhard Hansen

• Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

autor

Tomasz Jakubowski

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

Identyfikatory

DOI

10.4064/sm189-3-3