Abstract
The determinants of Gram-matrices defined by reproducing kernels can be averaged with respect to the arguments occuring. The results can be used to prove that, in a very general situation, interpolation points exist which furnish small Lagrange elements. The results are complementary to Auerbach’s Theorem. They apply even in cases where interpolation takes place on noncompact sets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
König H., Norms of minimal projections, J. Funct. Anal. 119 (1994), 253–280.
Lau T.-S., On an extremal problem of Fejér, J. Approx. Theory 53 (1988), 184–194.
Lubinsky D. S., Ideas of weighted approximations on (-∞,∞), in Approximation Theory VIII (C. K. Chui, L. L. Schumaker, eds.), World Scientific, Singapore, 1995, 371–396.
Reimer M., Constructive theory of multivariate functions. BI-Wisenschafts-verlag, Mannheim, 1990.
Sansone G., Orthogonal functions. Interscience Publ., London, 1959, 322, 323.
Taylor A. E., A geometric theorem and its application to biorthogonal systems, Bull. Amer. Math. Soc. 53 (1947), 614–616.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Basel AG
About this paper
Cite this paper
Reimer, M. (1997). The Average Size of Certain Gram-Determinants and Interpolation on Non-Compact Sets. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds) Multivariate Approximation and Splines. ISNM International Series of Numerical Mathematics, vol 125. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8871-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8871-4_19
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9808-9
Online ISBN: 978-3-0348-8871-4
eBook Packages: Springer Book Archive