Strictly positive definite functions on a compact group
HTML articles powered by AMS MathViewer
- by Mohamed Allali and Tomasz Przebinda PDF
- Proc. Amer. Math. Soc. 129 (2001), 1459-1462 Request permission
Abstract:
We recognize a result of Schreiner, concerning strictly positive definite functions on a sphere in an Euclidean space, as a generalization of Bochner’s theorem for compact groups.References
- J. Dieudonné, Éléments d’analyse. Tome VI. Chapitre XXII, Cahiers Scientifiques, Fasc. XXXIX, Gauthier-Villars Éditeur, Paris, 1975 (French). MR 0621690
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
- A. A. Kirillov, Elements of the theory of representations, Grundlehren der Mathematischen Wissenschaften, Band 220, Springer-Verlag, Berlin-New York, 1976. Translated from the Russian by Edwin Hewitt. MR 0412321
- C. Müller, Analysis of Spherical Symmetries in Euclidean Spaces, Springer-Verlag, New York, 1998.
- Michael Schreiner, On a new condition for strictly positive definite functions on spheres, Proc. Amer. Math. Soc. 125 (1997), no. 2, 531–539. MR 1353398, DOI 10.1090/S0002-9939-97-03634-4
Additional Information
- Mohamed Allali
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- Address at time of publication: Department of Computer Science, Mathematics and Physics, Chapman University, Orange, California 92866
- Email: mallali@crystal.math.ou.edu
- Tomasz Przebinda
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- MR Author ID: 257122
- Received by editor(s): December 18, 1998
- Received by editor(s) in revised form: August 30, 1999
- Published electronically: October 24, 2000
- Additional Notes: This research was partially supported by NSF Grant DMS 9622610.
- Communicated by: Roe Goodman
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1459-1462
- MSC (1991): Primary 43A35, 43A90, 42A82, 41A05
- DOI: https://doi.org/10.1090/S0002-9939-00-05687-2
- MathSciNet review: 1814173