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arXiv · 2109.01837

On the Green function of the killed fractional Laplacian on the periodic domain

Thomas Simon
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Abstract

We give a very simple proof of the positivity and unimodality of the Green function for the killed fractional Laplacian on the periodic domain. The argument relies on the Jacobi triple product and a probabilistic representation of the Green function. We also show by a contour integration that the Green function is completely monotone on the positive part of the periodic domain.

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Thomas Simon. 2021-09-04. On the Green function of the killed fractional Laplacian on the periodic domain. https://doi.org/10.1515/fca-2021-0069

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