Characterization of sharp global Gaussian estimates for Schr\"odinger heat kernels

Jacek Dziuba\'nski; Karol Szczypkowski; Krzysztof Bogdan

arxiv: 1606.03745 · v1 · pith:46GD3A6Mnew · submitted 2016-06-12 · 🧮 math.FA · math.AP

Characterization of sharp global Gaussian estimates for Schr\"odinger heat kernels

Krzysztof Bogdan , Jacek Dziuba\'nski , Karol Szczypkowski This is my paper

classification 🧮 math.FA math.AP

keywords characterizationgaussianglobalodingerschrsharpboundscondition

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We investigate when the fundamental solution of the Schr\"odinger equation $\partial_t=\Delta+V$ posseses sharp Gaussian bounds global in space and time. We give a characterization for $V\leq 0$ and a sufficient condition for general $V$.

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Characterization of sharp global Gaussian estimates for Schr\"odinger heat kernels

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