Sampling and interpolation on some nilpotent Lie groups
type: Item
instance of: scholarly article
title: Sampling and interpolation on some nilpotent Lie groups
zbMATH Open document ID: 1334.22009
published in: Forum Mathematicum
publication date: 2016-03-08T00:00:00Z
full work available at URL: https://vc.bridgew.edu/math_fac/60
review text: This paper deals with sampling spaces. The simplest example of such spaces with interpolation property over a nilpotent Lie group is provided by the well-known Whittaker, Shannon, Kotelnikov theorem, although the first example of a sampling space with interpolation property on a noncommutative nilpotent Lie group was defined over the three-dimensional Heisenberg Lie group by Currey and Mayely using the Plancherel transform. However, the question of existence of sampling spaces with interpolation property on some non-commutative nilpotent Lie groups is a challenging problem which constitutes the main focus of this paper, which is, in fact a generalization of recent results obtained for the Heisenberg group by \textit{B. Currey} and \textit{A. Mayeli} [Rocky Mt. J. Math. 42, No. 4, 1135--1151 (2012; Zbl 1271.42042)]. Indeed, the author, by using well-known facts from time-frequency analysis, provides some precise sufficient conditions for the existence of sampling spaces with the interpolation property, with respect to some discrete subset of a non-commutative, simply connected, connected, two-step nilpotent Lie group with Lie algebra verifying certain conditions. The author also computes several explicit examples.
reviewed by: Juan Núñez Valdés
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 22E27
zbMATH DE Number: 6551636
zbMATH Keywords: sampling
zbMATH Keywords: interpolation
zbMATH Keywords: nilpotent Lie groups
zbMATH Keywords: representations
MaRDI profile type: Publication
OpenAlex ID: W2329977297
Wikidata QID: Q115236421
DOI: 10.1515/FORUM-2014-0035
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description: scientific article; zbMATH DE number 6551636