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arXiv · 1903.00521

The Fractional Laplacian has Infinite Dimension

Adrian Spener·Frederic Weber·Rico Zacher
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Abstract

We show that the fractional Laplacian on $\mathbb{R}^d$ fails to satisfy the Bakry-\'Emery curvature-dimension inequality $CD(\kappa,N)$ for all curvature bounds $\kappa\in \mathbb{R}$ and all finite dimensions $N>0$.

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Adrian Spener, Frederic Weber, Rico Zacher. 2019-03-01. The Fractional Laplacian has Infinite Dimension. https://arxiv.org/abs/1903.00521

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