Strictly positive definite functions on compact abelian groups
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- by Jan Emonds and Hartmut Führ PDF
- Proc. Amer. Math. Soc. 139 (2011), 1105-1113 Request permission
Abstract:
We study the Fourier characterisation of strictly positive definite functions on compact abelian groups. Our main result settles the case $G = F \times \mathbb {T}^r$, with $r \in \mathbb {N}$ and where $F$ is a finite abelian group. The characterisation obtained for these groups does not extend to arbitrary compact abelian groups; it fails in particular for all torsion-free groups.References
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Additional Information
- Jan Emonds
- Affiliation: Institut für Mathematik, Universität Paderborn, D-33098 Paderborn, Germany
- Email: emonds@math.upb.de
- Hartmut Führ
- Affiliation: Lehrstuhl A für Mathematik, RWTH Aachen, D-52056 Aachen, Germany
- Email: fuehr@matha.rwth-aachen.de
- Received by editor(s): February 15, 2010
- Received by editor(s) in revised form: April 9, 2010
- Published electronically: August 10, 2010
- Additional Notes: The first author was supported by the DFH and the International Research Training Group DFG-1133 “Geometry and Analysis of Symmetries”
- Communicated by: Michael T. Lacey
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 1105-1113
- MSC (2010): Primary 43A25; Secondary 43A75
- DOI: https://doi.org/10.1090/S0002-9939-2010-10533-6
- MathSciNet review: 2745662