A Density Condition for Interpolation on the Heisenberg Group

Details A Density Condition for Interpolation on the Heisenberg Group A Density Condition for Interpolation on the Heisenberg Group

2010-07-23

arxiv.org/abs/1007.4043v1

Mathematics

Representation Theory

Scientific paper

Let $N$ be the Heisenberg group. We consider left-invariant multiplicity free subspaces of $L^2(N)$. 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.

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