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2014 Bandlimited spaces on some 2-step nilpotent Lie groups with one Parseval frame generator
Vignon Oussa
Rocky Mountain J. Math. 44(4): 1343-1366 (2014). DOI: 10.1216/RMJ-2014-44-4-1343

Abstract

Let $N$ be a step two connected and simply connected non commutative nilpotent Lie group which is square-integrable modulo the center. Let $Z$ be the center of $N$. Assume that $N=P\rtimes M$ such that $P$ and $M$ are simply connected, connected abelian Lie groups, $P$ is a maximal normal abelian subgroup of $N$, $M$ acts non-trivially on $P$ by automorphisms and $\dim P/Z=\dim M$. We study bandlimited subspaces of $L^2(N)$ which admit Parseval frames generated by discrete translates of a single function. We also find characteristics of bandlimited subspaces of $L^2(N)$ which do not admit a single Parseval frame. We also provide some conditions under which continuous wavelets transforms related to the left regular representation admit discretization, by some discrete set $\Gamma\subset N$. Finally, we show some explicit examples in the last section.

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Vignon Oussa. "Bandlimited spaces on some 2-step nilpotent Lie groups with one Parseval frame generator." Rocky Mountain J. Math. 44 (4) 1343 - 1366, 2014. https://doi.org/10.1216/RMJ-2014-44-4-1343

Information

Published: 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1304.42080
MathSciNet: MR3274352
Digital Object Identifier: 10.1216/RMJ-2014-44-4-1343

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.44 • No. 4 • 2014
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