Interpolation on the complex Hilbert sphere using positive definite and conditionally negative definite kernels

Acta Mathematica Hungarica

Volumn 75, Issue 3, 1997, Pages 215-225

  Menegatto, V A ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031285763     PISSN: 02365294     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006599221736     Document Type: Article

References (16)

1. E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag (Berlin, 1971).
2. C. Berg, J. P. R. Christensen, and P. Ressel, Harmonic Analysis on Semigroups, Springer-Verlag (New York, 1984).
3. E. W. Cheney, Approximation using positive definite functions, in Approximation Theory VII, Charles K. Chui and Larry L. Schumaker Eds., World Scientific Publishing Co., Inc., 1995.
4. J. P. R. Christensen and P. Ressel, Positive definite kernels on the complex Hilbert sphere, Math. Z., 180 (1982), 193-201.
5. G. E. Fasshauer, Radial basis functions on spheres, PhD Dissertation, Vanderbilt University, 1995.
6. R. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press (Cambridge, 1989).
7. W. R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions, Approx. Theory Appl., 4 (1988), 77-89.
8. V. A. Menegatto, Interpolation on the complex Hilbert sphere, Approx. Theory Appl., 12-2 (1996), 31-39.
9. V. A. Menegatto, Strictly positive definite kernels on the Hilbert sphere, Appl. Anal., 55 (1994), 91-101.
10. C. A. Micchelli, Interpolation of scattered data: distance matrices and conditionally positive definite functions, Constr. Approx., 2 (1986), 11-22.
11. A. Oppenheim, Inequalities connected with definite hermitian forms, J. London Math. Soc., 5 (1930), 114-119.
12. A. Ostrowski and O. Taussky, On the variation of the determinant of a positive definite matrix, Nederl. Akad. Wet. Proc. (A), 54 (1951), 383-385.
13. G. Pólya and G. Szego, Problems and Theorems in Analysis II, Springer-Verlag (New York, 1976).
14. I. J. Schoenberg, Metric spaces and completely monotone functions, Ann. Math., 39 (1938), 811-841.
15. X. Sun and E. W. Cheney, Fundamental sets of continuous functions on spheres, Constructive Approximation, to appear.
16. D. V. Widder, The Laplace Transform, Princeton University Press (Princeton, 1946).