Improper Poisson integral of the sinc function

2025/04/08 by Jerzy Szulga, Szulga, Jerzy
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Point processes and geometric inequalities #Primary 60H05. Secondary 60F25 #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2504.05574

openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A formal sum ∑_n f(S_n) may be seen as the integral ∫ f dN with respect to random point process N(A)=|\n:S_n∈ A\|. We study its convergence beyond the well known context of Lebesgue integrable functions, admitting nonintegrable functions whose improper Riemann-Lebesgue integrals exist. We focus on the sinc function and some of its relations leaving the general case to conjectures.

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