Divergence of Lagrange interpolation on a set of second category
✍ Scribed by P. Vértesi
- Book ID
- 105409967
- Publisher
- Akadmiai Kiad
- Year
- 1984
- Tongue
- English
- Weight
- 633 KB
- Volume
- 43
- Category
- Article
- ISSN
- 1588-2632
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📜 SIMILAR VOLUMES
It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to \(|x|\) at equally spaced nodes in \([-1,1]\) diverges everywhere, except at zero and the end-points. In the present paper we show that the case of equally spaced nodes is not an exceptional one in this
Given a compact interval 2, it is shown that for E. A. Rakhmanov's weight w on 2 which is bounded from below by the Chebyshev weight v on 2 (1982, Math. USSR Sb. 42, 263) the corresponding orthonormal polynomials are unbounded in every L p v (and L p w ) with p>2 and also that the Lagrange interpola