A negative answer to problem 10 of P. Turán (Q1352334)
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scientific article; zbMATH DE number 978034
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A negative answer to problem 10 of P. Turán |
scientific article; zbMATH DE number 978034 |
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A negative answer to problem 10 of P. Turán (English)
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13 February 1997
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A weight \(w(x)\) is provided with the properties: \(w(x)\geq(1- x^2)^{-1/2}\) and Lagrange's interpolation based on the zeros of orthogonal polynomials with respect to \(w\) diverges in \(L_p\) \((p>6)\) for some \(f\in C[-1,1]\). This gives a negative answer to Problem 10 of P. Turán.
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Lagrange's interpolation
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0.8526098
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0.85082316
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0.8446337
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0.8428174
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0.8130831
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