Linear Dependency of Translations and Square Integrable Representations
Functional Analysis
2017-10-18 v2 Group Theory
Abstract
Let be a locally compact group. We examine the problem of determining when nonzero functions in have linearly independent translations. In particular, we establish some results for the case when has an irreducible, square integrable, unitary representation. We apply these results to the special cases of the affine group, the shearlet group and the Weyl-Heisenberg group. We also investigate the case when has an abelian, closed subgroup of finite index.
Keywords
Cite
@article{arxiv.1509.00493,
title = {Linear Dependency of Translations and Square Integrable Representations},
author = {Peter A. Linnell and Michael J. Puls and Ahmed Roman},
journal= {arXiv preprint arXiv:1509.00493},
year = {2017}
}
Comments
A simplified proof for Theorem 1.6, fixed some typos