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Notes on Steklov's Conjecture inLpand on Divergence of Lagrange Interpolation inLp

✍ Scribed by Paul Nevai; Ying Guang Shi

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 248 KB
Volume: 90
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1996.3068

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✦ Synopsis

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 interpolation process based on their zeros diverges in every L p v with p>2 for some continuous f . This yields an affirmative answer to Conjecture 2.9 in ``Research Problems in

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