A necessary and sufficient condition for strictly positive definite functions on spheres
HTML articles powered by AMS MathViewer
- by Debao Chen, Valdir A. Menegatto and Xingping Sun PDF
- Proc. Amer. Math. Soc. 131 (2003), 2733-2740 Request permission
Abstract:
We give a necessary and sufficient condition for the strict positive-definiteness of real and continuous functions on spheres of dimension greater than one.References
- Richard Askey, Orthogonal polynomials and special functions, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. MR 0481145
- V. A. Menegatto, Strictly positive definite functions on spheres, Ph.D. Dissertation, University of Texas-Austin, 1992.
- Valdir A. Menegatto, Strictly positive definite kernels on the circle, Rocky Mountain J. Math. 25 (1995), no. 3, 1149–1163. MR 1357116, DOI 10.1216/rmjm/1181072211
- Valdir A. Menegatto, Strictly positive definite kernels on the Hilbert sphere, Appl. Anal. 55 (1994), no. 1-2, 91–101. MR 1379646, DOI 10.1080/00036819408840292
- Amos Ron and Xingping Sun, Strictly positive definite functions on spheres in Euclidean spaces, Math. Comp. 65 (1996), no. 216, 1513–1530. MR 1370856, DOI 10.1090/S0025-5718-96-00780-6
- A. Ron and X. Sun, Strictly positive definite functions on spheres, CMS TR 94-6, University of Wisconsin-Madison, February 1994.
- Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
- 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
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
- Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
- Yuan Xu and E. W. Cheney, Strictly positive definite functions on spheres, Proc. Amer. Math. Soc. 116 (1992), no. 4, 977–981. MR 1096214, DOI 10.1090/S0002-9939-1992-1096214-6
Additional Information
- Debao Chen
- Affiliation: Department of Computer Sciences, Oklahoma State University-Tulsa, Tulsa, Oklahoma 74106
- Email: cdebao@cs.okstate.edu
- Valdir A. Menegatto
- Affiliation: ICMC-Universidade de Sao Paulo, Caixa Postal 668, 13560-970 Sao Carlos SP, Brasil
- MR Author ID: 358330
- ORCID: 0000-0002-4213-8759
- Email: menegatt@icmc.usp.br
- Xingping Sun
- Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
- Email: xis280f@smsu.edu
- Received by editor(s): March 16, 2001
- Received by editor(s) in revised form: January 29, 2002
- Published electronically: April 7, 2003
- Communicated by: Andreas Seeger
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2733-2740
- MSC (2000): Primary 41A05, 42A15; Secondary 33C45, 33C55
- DOI: https://doi.org/10.1090/S0002-9939-03-06730-3
- MathSciNet review: 1974330