Abstract
Let U ⊂ C(D) be an arbitrary n-dimensional linear subspace of continuous functions on a compact set D ⊂ ℝS. We construct interpolation operators L : C(D) → U which have an operator norm ≥ √n — 1.
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Schoenberg I. J. and Whitney A., On Pólya frequency functions III. The positivity of translation determinants with applications to the interpolation problem by spline curves. Trans. Amer. Math. Soc. 74, (1953), 246–259.
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© 1997 Springer Basel AG
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von Golitschek, M. (1997). Interpolation by Continuous Function Spaces. 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_7
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DOI: https://doi.org/10.1007/978-3-0348-8871-4_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9808-9
Online ISBN: 978-3-0348-8871-4
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