Abstract
In this paper we obtain the strong asymptotics for the sequence of orthogonal polynomials with respect to the inner product\(\left\langle {f,g} \right\rangle s = \sum\limits_{k - 0}^m {\int\limits_{\Delta _k } {f^{\left( k \right)} \left( x \right)g^{\left( k \right)} \left( x \right)d\mu \kappa } } \left( x \right)\) where\(\left\{ {\mu _\kappa } \right\}_{k = 0}^m ,m \in \mathbb{Z}_ + \), are measures supported on [−1,1] which satisfy Szegö's condition.
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Research partially supported by a research grant from Dirección General de Enseñanza Superior (DGES) of Spain, project code PB95-1205, by INTAS project 93-219-ext, and by Junta de Andalucía, Grupo de Investigación FQM 0229.
Research carried out under grant from Agencia Española de Cooperación Internacional and Doctoral Program of the Universidad Carlos III de Madrid (Spain).
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Finkelshtein, A.M., Cabrera, H.P. Strong asymptotics for Sobolev orthogonal polynomials. J. Anal. Math. 78, 143–156 (1999). https://doi.org/10.1007/BF02791131
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DOI: https://doi.org/10.1007/BF02791131