On the exact constant in the \(L_2\) Markov inequality (Q2425416)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the exact constant in the \(L_2\) Markov inequality |
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On the exact constant in the \(L_2\) Markov inequality (English)
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5 May 2008
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The author presents an elementary method for treating the problem of maximizing \(\| q'_n\| _2/\| q_n\| _2\), the \(L^2(-1,1)\)-norm of the derivative of normalized polynomials \(q_n\) of degree at most \(n\). The method leads to a representation of the extremal polynomial as a combination of the derivatives of the Legendre polynomial of degree \(n+1\).
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Markov inequality
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\(L_2\)-norm
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Legendre polynomials
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