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arXiv · 2504.08108

Periodic homogenization of convolution type operators with heavy tails

Andrey Piatnitski·Elena Zhizhina
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Abstract

The paper deals with periodic homogenization of nonlocal symmetric convolution type operators in $L^2(\mathbb R^d)$, whose kernel is the product of a density that belongs to the domain of attraction of an $\alpha$-stable law and a rapidly oscillating positive periodic function. Assuming that the local oscillation of the said density satisfies a proper upper bound at infinity, we prove homogenization result for the studied family of operators.

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Andrey Piatnitski, Elena Zhizhina. 2025-04-10. Periodic homogenization of convolution type operators with heavy tails. https://arxiv.org/abs/2504.08108

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