Direct form seminorms arising in the theory of interpolation by translates of a basis function

Advances in Computational Mathematics

Volumn 11, Issue 2-3, 1999, Pages 161-182

  Levesley, Jeremy ^a   Light, Will ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033443790     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018971808961     Document Type: Article

References (11)

1. R.A. Adams, Sobolev Spaces (Academic Press, New York, 1978).
2. m-splines, RAIRO Anal. Numer. 12(4) (1978) 325-334.
3. J. Duchon, Splines minimising rotation-invariant seminorms in Sobolev spaces, in: Constructive Theory of Functions of Several Variables, Lecture Notes in Mathematics, Vol. 571, eds. W. Schempp and K. Zeller (Springer, Berlin, 1977) pp. 85-100.
4. L. Hörmander, The Analysis of Linear Partial Differential Operators I (Springer, Berlin, 1983).
5. W.A. Light and H.S.J. Wayne, Some aspects of radial basis function approximation, in: Approximation Theory, Spline Functions and Applications, ed. S.P. Singh (Kluwer Academic, Dordrecht, 1995) pp. 163-190.
6. W.A. Light and H.S.J. Wayne, Spaces of distributions, interpolation by translates of a basis function, and error estimates, Numer. Math. 81 (1999) 415-450.
7. W. Madych and S. Nelson, Multivariate interpolation and conditionally positive definite functions, Approx. Theory Appl. 4 (1988) 77-89.
8. W.R. Madych and S.A. Nelson, Multivariate interpolation and conditionally positive definite functions II, Math. Comp. 54 (1990) 211-230.
9. W. Rudin, Functional Analysis (McGraw-Hill, New York, 1973).
10. W. Rudin, Real and Complex Analysis (McGraw-Hill, New York, 1970).
11. R. Schaback, Multivariate interpolation and approximation by translates of a basis function, in: Approximation Theory VIII, Vol. I: Approximation and Interpolation, eds. C.K. Chui and L.L. Schumaker (World Scientific, Singapore, 1995) pp. 491-514.