Positive positivedefinite functions and measures on locally compact abelian groups
Abstract
The author was recently able to provide a cohomological interpretation of Tate's RiemannRoch formula for number fields using some new harmonic analysis objects, ghostspaces. When trying to investigate these objects in general, we realized the importance of functions and measures on locally compact abelian groups that are both positive and positivedefinite at the same time. It looks like this class of functions and measures was not systematically studied before. The goal of this paper is to partially fill in this gap. We answer some of the natural questions involving these functions and measures, especially those that satisfy some extra integrability conditions. We also study some operations and constructions involving these functions and measures. There are several very interesting open questions, that we are only able to point out at this moment. In particular, the structure of the cone of such functions is not clear even when the group is just $\R.$
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:math/9906126
 Bibcode:
 1999math......6126B
 Keywords:

 Mathematics  Functional Analysis
 EPrint:
 12 pages