Strict positive definiteness on spheres via disk polynomials

International Journal of Mathematics and Mathematical Sciences

Volumn 31, Issue 12, 2002, Pages 715-724

  Menegatto, V A ^a   Peron, A P ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b STATE UNIVERSITY OF MARINGÁ   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3242666398     PISSN: 01611712     EISSN: None     Source Type: Journal    
DOI: 10.1155/S0161171202108076     Document Type: Article

References (16)

1. C. Berg, J. P. R. Christensen, and P. Ressel, Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions, Graduate Texts in Mathematics, vol. 100, Springer-Verlag, New York, 1984. MathSciNet. Zentralblatt für Mathematik.
2. J. N. Boyd, Orthogonal polynomials on the disc, Thesis, University of Virginia, Virginia, 1972.
3. J. N. Boyd and P. N. Raychowdhury, Zonal harmonic functions from two-dimensional analogs of Jacobi polynomials, Applicable Anal. 16 (1983), no. 3, 243-259. MathSciNet. Zentralblatt für Mathematik.
4. E. W. Cheney, Approximation using positive definite functions, Approximation Theory VIII, Vol. 1 (College Station, Tex, 1995), Series in Approximations and Decompositions, vol. 6, World Scientific Publishing, New Jersey, 1995, pp. 145-168. MathSciNet.
5. E. W. Cheney and W. A. Light, A Course in Approximation Theory, Brooks/Cole Publishing, California, 1999.
6. E. W. Cheney and X. Sun, Interpolation on spheres by positive definite functions, Approximation Theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 212, Dekker, New York, 1998, pp. 141-156. MathSciNet. Zentralblatt für Mathematik.
7. J. P. R. Christensen and P. Ressel, Positive definite kernels on the complex Hilbert sphere, Math. Z. 180 (1982), no. 2, 193-201. MathSciNet. Zentralblatt für Mathematik.
8. G. E. Fasshauer and L. L. Schumaker, Scattered data fitting on the sphere, Mathematical Methods for Curves and Surfaces, II (Lillehammer, 1997), Innovations in Applied Mathematics, Vanderbilt University Press, Tennessee, 1998, pp. 117-166. MathSciNet. Zentralblatt für Mathematik.
9. T. H. Koornwinder, The addition formula for Jacobi polynomials II. The Laplace type integral representation and the product formula, Tech. Report TW 133, Math. Centrum, Amsterdam, 1972. Zentralblatt für Mathematik.
10. V. A. Menegatto and A. P. Peron, A complex approach to strict positive definiteness on spheres, Integral Transform. Spec. Funct. 11 (2001), no. 4, 377-396. MathSciNet.
11. V. A. Menegatto and A. P. Peron, Positive definite kernels on complex spheres, J. Math. Anal. Appl. 254 (2001), no. 1, 219-232. CrossRef. MathSciNet. Zentralblatt für Mathematik.
12. F. J. Narcowich, Recent developments in approximation via positive definite functions, Approximation Theory IX, Vol. 2 (Nashville, Tenn, 1998), Innovations in Applied Mathematics, Vanderbilt University Press, Tennessee, 1998, pp. 221-242. MathSciNet. Zentralblatt für Mathematik.
13. R. L. Šapiro, Irreducible representations of the group $/mathrm(su) (n) $ of class $1$ with respect to $\mathrm(su) (n-1) $, Uspehi Mat. Nauk 22 (1967), no. 1(133), 180-182.
14. R. L. Šapiro, Special functions connected with representations of the group $\mathrm(SU) (n) $ of class I relative to $\mathrm(SU) (n-1) (n\geq 3)$, Amer. Math. Soc. Transl. (2) (1979), no. 113, 201-211. Zentralblatt für Mathematik.
15. X. Sun and V. A. Menegatto, Strictly positive definite functions on the complex Hilbert sphere, Adv. Comput. Math. 11 (1999), no. 2-3, 105-119. MathSciNet. Zentralblatt für Mathematik.
16. N. Ya. Vilenkin and R. L. Šapiro, Irreducible representations of the group $\mathrm(SU) (n) $ of class I relative to $\mathrm(SU) (n-1) $, Izv. Vysš. Učebn. Zaved. Matematika 1967 (1967), no. 7(62), 9-20.