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- W2565851963 abstract "We refer to a pair of non trivial probability measures $$(mu _{0},mu _{1})$$ supported on the unit circle as a coherent pair of measures of the second kind on the unit circle if the corresponding sequences of monic orthogonal polynomials $${Phi _{n}(mu _0;z)}_{nge 0}$$ and $${Phi _{n}(mu _1;z)}_{nge 0}$$ satisfy $$frac{1}{n} Phi _{n}^{prime }(mu _0; z) = Phi _{n-1}(mu _1; z) - chi _n Phi _{n-2}(mu _1; z)$$ , $$n ge 2$$ . It turns out that there are more interesting examples of pairs of measures on the unit circle with this latter coherency property than in the case of the standard coherence. The main objective in this contribution is to determine such pairs of measures. The polynomials orthogonal with respect to the Sobolev inner products associated with coherent pairs of measures of the second kind are also studied." @default.
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- W2565851963 date "2016-12-19" @default.
- W2565851963 modified "2023-10-04" @default.
- W2565851963 title "Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind" @default.
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- W2565851963 doi "https://doi.org/10.1007/s00025-016-0631-y" @default.
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