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Strictly positive definite functions on a compact group
Author(s):
Mohamed
Allali;
Tomasz
Przebinda
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1459-1462.
MSC (1991):
Primary 43A35, 43A90, 42A82, 41A05
Posted:
October 24, 2000
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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:
-
- [D]
- J. Dieudonné, Éléments d'Analyse, Gauthier-Villars Éditeur, Paris/Bruxelles/Montréal, 1975. MR 58:29825a
- [H-R]
- E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Volume II, Springer-Verlag, New York, 1970. MR 41:7378
- [K]
- A. A. Kirillov, Elements of the Theory of Representations, Springer-Verlag, New York, 1976. MR 54:447
- [M]
- C. Müller, Analysis of Spherical Symmetries in Euclidean Spaces, Springer-Verlag, New York, 1998. CMP 98:05
- [S]
- M. Schreiner, On a New Condition For Strictly Positive Definite Functions On Spheres, Proceedings of the AMS 125 (1997), 531-539. MR 97d:43005
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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
DOI:
10.1090/S0002-9939-00-05687-2
PII:
S 0002-9939(00)05687-2
Keywords:
Positive definite functions,
Bochner's theorem
Received by editor(s):
December 18, 1998
Received by editor(s) in revised form:
August 30, 1999
Posted:
October 24, 2000
Additional Notes:
This research was partially supported by NSF Grant DMS 9622610.
Communicated by:
Roe Goodman
Copyright of article:
Copyright
2000,
American Mathematical Society
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