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On the Converse Inequality of Markov Type inL2Norm

✍ Scribed by Weiyu Chen

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
117 KB
Volume
200
Category
Article
ISSN
0022-247X

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✦ Synopsis

The converse inequality of Markov type is discussed in this note. The main result says that the best possible constant for this inequality is the square root of the least eigenvalue of a certain positive definite matrix. As applications of the main result, the Laguerre weight and Hermite weight are investigated in detail, and the best constants in these two cases are obtained explicitly.

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Markov′s Inequality and Zeros of Orthogo
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✍ A. Jonsson 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 378 KB

Zeros of orthogonal polynomials defined with respect to general measures are studied. It is shown that a certain estimate for the minimal distance between zeros holds if and only if the support \(F\) of the measure satisfies a homogeneity condition and Markov's inequality holds on \(F\). C 1994 Acad