Averages on annuli of Eulidean space
Emmanuel Lesigne (LMPT), Fran\c{c}ois Havard (LMPT)
TL;DR
This paper investigates the conditions under which differentiation and ergodic theorems hold for averages taken over thick spherical shells in Euclidean space, contributing to understanding their applicability in harmonic analysis and ergodic theory.
Contribution
It introduces new results on the validity range of differentiation and ergodic theorems for averages on annuli in Euclidean space, extending classical theorems to these geometric settings.
Findings
Established conditions for differentiation theorems on thick spheres
Extended ergodic theorems to averages on annuli in
Identified limitations of these theorems in Euclidean space
Abstract
We study the range of validity of differentiation theorems and ergodic theorems for actions, for averages on "thick spheres" of Euclidean space.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematics and Applications · Holomorphic and Operator Theory