A criterion for a power-law rate of convergence of ergodic means for unitary actions of ℤ^{𝕕} and ℝ^{𝕕}

Ivan Viktorovich Podvigin

doi:10.1090/spmj/1874

A criterion for a power-law rate of convergence of ergodic means for unitary actions of ℤ^{𝕕} and ℝ^{𝕕}

St Petersburg Mathematical Journal 2026

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Authors: Ivan Viktorovich Podvigin

DOI: 10.1090/spmj/1874

Cited by: 1

References: 23

Abstract

For averages over parallelepipeds of unitary actions of the groups R d \mathbb {R}^d and Z d {\mathbb {Z}^d} , a criterion for a power rate of convergence in norm with all possible exponents is obtained. The proof is based on the asymptotics of the integrals of product of cardinal sines.

Fields of Study & Subjects

Advanced Operator Algebra Research Advanced Harmonic Analysis Research Limits and Structures in Graph Theory

Publication details

Journal / source: St Petersburg Mathematical Journal
Publisher: American Mathematical Society (AMS)
Volume: 36
Issue: 4
Pages: 607–618
Publication date: 6 January 2026
Language: EN

References 23