A family of Nikishin systems with periodic recurrence coefficients (Q2842982)
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scientific article; zbMATH DE number 6197055
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A family of Nikishin systems with periodic recurrence coefficients |
scientific article; zbMATH DE number 6197055 |
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A family of Nikishin systems with periodic recurrence coefficients (English)
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9 August 2013
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multiple orthogonal polynomial
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Nikishin system
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block Toeplitz matrix
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Hermite-Padé approximant
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strong asymptotics
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ratio asymptotics
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For a Nikishin system of \(p\) measures, the corresponding sequence of multiple orthogonal polynomials satisfies a \((p+2)\)-term recurrence relation, whose recurrence coefficients have periodic limits of period \(p\), under appropriate assumptions. The authors take these limits as the coefficients of a new recurrence relation, and construct the so-called Chebyshev-Nikishin polynomials. These polynomials form a sequence of multiple orthogonal polynomials with respect to a Nikishin system whose measures are absolute continuous on their corresponding intervals.
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