Erratum: "Approximation in rough native spaces by shifts of smooth kernels on spheres" (Journal of Approximation Theory (2005) vol. 133 (269-283) 10.1016/j.jat.2004.12.005);Approximation in rough native spaces by shifts of smooth kernels on spheres

Journal of Approximation Theory

Volumn 133, Issue 2, 2005, Pages 269-283

  Levesley, J ^a   Sun, X ^b  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b MISSOURI STATE UNIVERSITY   (United States)

Author keywords

Native space; Radial basis function; Reproducing kernels

Indexed keywords

EID: 14944384628     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2005.11.002     Document Type: Erratum

References (22)

1. S. Bochner Hilbert distances and positive definite functions Ann. of Math. 42 1941 647-656
2. D. Chen V.A. Menegatto X. Sun A necessary and sufficient condition for strictly positive definite functions on spheres Proc. Amer. Math. Soc. 131 2003 2733-2740
3. Z. Ditzian Fractional derivatives and best approximation Acta. Math. Hungar. 81 4 1998 323-348
4. N. Dyn F. Narcowich J. Ward Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold Constr. Approx. 15 1999 175-208
5. M. von Golitschek W. Light Interpolation by polynomials and radial basis functions on spheres Constr. Approx. 17 2001 1-18
6. K. Jetter J. Stöckler J.D. Ward Error estimates for scattered data interpolations on spheres Math. Comp. 68 1999 733-747
7. J. Levesley, W. A. Light, D. Rogozin, X. Sun, A simple approach to variational theory for interpolation on spheres, International Theory of Numerical Analysis, vol. 132, Birkhauser, Verlag Base/Switerzland, 1999.
8. V.A. Menegatto Strictly positive definite kernels on the Hilbert spheres Appl. Anal. 55 1994 114-119
9. V.A. Menegatto Interpolation on the complex Hilbert sphere Approx. Theory Appl. 11 1995 1-9
10. F.J. Narcowich Generalized Hermite interpolation and positive definite kernels on a Riemannian manifold J. Math. Anal. Appl. 190 1995 165-193
11. F.J. Narcowich R. Schaback J.D. Ward Approximation in Sobolev spaces by kernel expansions J. Approx. Theory 114 2002 70-83
12. F.J. Narcowich, J.D. Ward, Scattered data interpolation on sphere: Error estimates and locally supported basis functions, SIAM J. Math. Anal. 36 (2004) 284-300.
13. D. Ragozin J. Levesley The fundamentality of translates of spherical functions on compact homogeneous spaces J. Approx. Theory 103 2000 252-268
14. A. Ron X. Sun Strictly positive definite functions on spheres Math. Comp. 65 1996 1513-1530
15. I.J. Schoenberg Positive definite functions on spheres Duke Math. J. 9 1942 96-108
16. R. Schaback Improved error bounds for scattered interpolation by radial basis functions Math. Comp. 68 1999 201-216
17. X. Sun, Strictly positive definite functions on the unit circle, Math. Comp. 74 (2005) 709-721.
18. X. Sun E.W. Cheney Fundamental sets of continuous functions on spheres Constr. Approx. 13 1997 245-250
19. E.M. Stein G. Weiss Introduction to Fourier Analysis on Euclidean Spaces 1971 Princeton University Press Princeton, NJ
20. G. Szego, Orthogonal Polynomials, fourth ed., American Mathematical Society Colloquium Publication, vol. 23, American Mathematical Society, Providence, RI, 1959.
21. Tanya M. Morton M. Neamtu Error bounds for solving pseudo-differential equations on spheres by collocation with zonal kernels J. Approx. Theory 114 2002 242-268
22. Y. Xu E.W. Cheney Strictly positive definite functions on spheres Proc. Amer. Math. Soc. 116 1992 977-981