Heisenberg uniqueness pairs and the Klein-Gordon equation

Details Heisenberg uniqueness pairs and the Klein-Gordon equation Heisenberg uniqueness pairs and the Klein-Gordon equation

2009-10-07

arxiv.org/abs/0910.1246v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

The notion of a Heisenberg Uniqueness Pair (HUP) is introduced. This amounts to asking which collections of exponentials are weak-star fundamental in $L^\infty$ on a planar curve. In the case when the curve is a hyperbola, we can give a complete answer if the frequencies are restricted to equally spaced points on a lattice-cross. As a consequence, we solve a problem on the density of algebras generated by two inner functions raised by Matheson and Stessin.

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