For groups which are the semidirect product of some vector group with a unimodular group we prove that the existence of a discrete frame obtained from an at-most countable set of vectors through the action of a given unitary representation implies that the representation in use has to be square-integrable.
On discrete frames associated with semidirect products / Aniello, P; Cassinelli, G; DE VITO, Ernesto; Levrero, A.. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - STAMPA. - 7:(2001), pp. 199-206. [10.1007/bf02510424]
On discrete frames associated with semidirect products
DE VITO, Ernesto;
2001
Abstract
For groups which are the semidirect product of some vector group with a unimodular group we prove that the existence of a discrete frame obtained from an at-most countable set of vectors through the action of a given unitary representation implies that the representation in use has to be square-integrable.
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