On Density of Generalized Polynomials
Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 202-207

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the density in C[a, b] of generalized polynomials of the form The main point of this note is that total positivity of K(x, t) has little relationship to density: There is a symmetric, analytic, totally positive (in fact ETP (∞)) kernel K for which these generalized polynomials are not dense.
DOI : 10.4153/CMB-1991-032-x
Mots-clés : Generalized polynomials, density, closure, totally positive kernels, positive kernels., 41A30, 41A35.
Dyn, N.; Lubinsky, D. S.; Shekhtman, Boris. On Density of Generalized Polynomials. Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 202-207. doi: 10.4153/CMB-1991-032-x
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[1] 1. Achiezer, N. I., Theory of Approximation, (transi, by C. J. Hyman), Ungar, New York, 1956. Google Scholar

[2] 2. Dyn, N. and Lubinsky, D. S., Convergence of Interpolation to Transforms of Totally Positive Kernels, Can. J. Math., 40 (1988), 750–768. Google Scholar

[3] 3. Gierz, G. and Shekhtman, B., A Duality Principle for Rational Approximation, Pacific J. Math., 125 (1986), 79–92. Google Scholar

[4] 4. Gierz, G. and Shekhtman, B., On Spaces with Large Chebyshev Subspaces, J. Approx. Th., 54 (1988), 155— 161. Google Scholar

[5] 5. Karlin, S., The Existence of Eigenvalues for Integral Operators, Trans. Amer. Math. Soc, 113 (1964), 1–17. Google Scholar

[6] 6. Karlin, S., Total positivity and convexity preserving transformations, Proc. Sympos. Pure Math., 7 (1963), 329–347. Google Scholar

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