Measures with locally finite support and spectrum
Abstract
An important problem in harmonic analysis is solved in this article: Is the Poisson summation formula unique or does it belong to a wider class? The latter is true. The method that is used to prove this statement is surprising. Our new Poisson's formulas were hidden inside an old and almost forgotten paper published in 1959 by A. P. Guinand. The role of number theory in this issue is fascinating.
- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- March 2016
- DOI:
- 10.1073/pnas.1600685113
- Bibcode:
- 2016PNAS..113.3152M