The classical Riemann localization principle states that if an integrable function of one variable vanishes in an open set, then its trigonometric Fourier expansion converges to zero in this set. This pointwise localization principle fails in higher dimensions. Here we study the Hausdorff dimension of the sets of point where localization for Riesz means for eigenfunction expansions of the Laplace-Beltrami operator on compact rank one symmetric spaces may fail
Colzani, L., Tenconi, M. (2017). Localization for Riesz means on compact rank one symmetric spaces. In Xuan Thinh Duong (Macquarie University) Christopher Meaney (Macquarie University) Lesley A. Ward (University of South Australia) (a cura di), Proceedings of the AMSI/AustMS 2014 Workshop in Harmonic Analysis and its Applications (pp. 26-49). Camberra : Centre for Mathematics and its Applications Mathematical Sciences Institute The Australian National University Camberra.
Localization for Riesz means on compact rank one symmetric spaces
Colzani, L
;Tenconi,M
2017
Abstract
The classical Riemann localization principle states that if an integrable function of one variable vanishes in an open set, then its trigonometric Fourier expansion converges to zero in this set. This pointwise localization principle fails in higher dimensions. Here we study the Hausdorff dimension of the sets of point where localization for Riesz means for eigenfunction expansions of the Laplace-Beltrami operator on compact rank one symmetric spaces may fail
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