Fractional Laplacians, perimeters and heat semigroups in Carnot groups
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DOI: 10.3934/dcdss.2018026
Abstract: We define and study the fractional Laplacian and the fractional perimeter of a set in Carnot groups and we compare the perimeter with the asymptotic behaviour of the fractional heat semigroup. read more here.
Keywords: heat semigroups; carnot groups; perimeters heat; laplacians perimeters ... See more keywords
Boundedness of Differential Transforms for Heat Semigroups Generated by Schrödinger Operators
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DOI: 10.4153/s0008414x20000097
Abstract: Abstract In this paper we analyze the convergence of the following type of series $$\begin{eqnarray}T_{N}^{{\mathcal{L}}}f(x)=\mathop{\sum }_{j=N_{1}}^{N_{2}}v_{j}\big(e^{-a_{j+1}{\mathcal{L}}}f(x)-e^{-a_{j}{\mathcal{L}}}f(x)\big),\quad x\in \mathbb{R}^{n},\end{eqnarray}$$ where ${\{e^{-t{\mathcal{L}}}\}}_{t>0}$ is the heat semigroup of the operator ${\mathcal{L}}=-\unicode[STIX]{x1D6E5}+V$ with $\unicode[STIX]{x1D6E5}$ being the classical laplacian, the… read more here.
Keywords: differential transforms; transforms heat; heat; heat semigroups ... See more keywords