Czasopismo
Tytuł artykułu
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Języki publikacji
Abstrakty
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.
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
235-254
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
- Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
autor
- Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
autor
- Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-3