Periodic homogenization of convolution type operators with heavy tails

2025/04/10 by Piatnitski, Andrey, Zhizhina, Elena
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2504.08108

Abstract

The paper deals with periodic homogenization of nonlocal symmetric convolution type operators in L²(\mathbb R^d), whose kernel is the product of a density that belongs to the domain of attraction of an α-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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