A DENSITY CONDITION FOR INTERPOLATION ON THE HEISENBERG GROUP

We consider left invariant multiplicity free subspaces of L²(N) where N is the Heisenberg group. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a class of discrete subsets of N that includes the integer lattice. W...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2012-01, Vol.42 (4), p.1135-1151
Main Authors: CURREY, BRADLEY, MAYELI, AZITA
Format: Article
Language:English
Subjects:
42C15
43A80
92A20
Fourier transformations
Gabor frame
Heisenberg group
Hilbert spaces
Integers
Interpolation
interpolation property
Mathematical functions
Mathematical lattices
Mathematical vectors
Mathematics
multiplicity free subspaces
sampling spaces
Sufficient conditions
Unit vectors
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Summary:We consider left invariant multiplicity free subspaces of L²(N) where N is the Heisenberg group. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a class of discrete subsets of N that includes the integer lattice. We exhibit a concrete example of a subspace that has interpolation for the integer lattice, and we also prove a necessary and sufficient condition for shift invariant subspaces to possess a singly-generated orthonormal basis of translates.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2012-42-4-1135