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Projections $ P$ on $ C=C[-1,1]$ which interpolate at $ \dim (P(C))$ or more points


Author: Chengmin Yang
Journal: Proc. Amer. Math. Soc. 115 (1992), 669-676
MSC: Primary 46E15; Secondary 41A65
DOI: https://doi.org/10.1090/S0002-9939-1992-1089415-4
MathSciNet review: 1089415
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Abstract: Let $ V$ be an $ n$ dimensional subspace of $ C[ - 1,1]$. This paper gives a necessary and sufficient condition for a bounded linear projection $ P$ from $ C[ - 1,1]$ onto $ V$ to have the property that $ Pf$ interpolates $ f$ at $ n$ or more points for any $ f \in C[ - 1,1]$.


References [Enhancements On Off] (What's this?)

  • [1] B. L. Chalmers, G. M. Philips, and P. J. Taylor, Polynomial approximation using projections whose kernel contain the Chebyshev polynomials, J. Approx. Theory 53 (1988), 321-334. MR 947435 (89f:41008)
  • [2] L. Narici and B. Edward Topological vector space, Marcel Dekker, New York, 1985. MR 812056 (87c:46003)
  • [3] F. Treves, Topological vector space, distributions and kernels, Academic Press, New York, 1967. MR 0225131 (37:726)
  • [4] C. Yang, WT measure vector spaces, preprint. MR 1232054 (94k:41044)
  • [5] R. Zielke, Discontinuous Cebysev system, Lecture Notes in Math., vol. 707, Springer-Verlag, Berlin and New York, 1970, MR 540207 (81a:41001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1089415-4
Keywords: Linear projection, WT measure vector space, interpolation, weak*-topology
Article copyright: © Copyright 1992 American Mathematical Society

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