Abstract
In this paper we study the behaviour of the quotient en(α)/en(β), where (en(α))−1/2 and (en(β))−1/2 are the leading coefficients of the orthonormal polynomials
and
on the unit circle U with respect to the measures α and β=α + ɛδ(t) (t∈U, ɛ>0, δ(t) the unit measure supported at z=t). By proving that it is possible to build a sequence of orthonormal polynomials over U with prescribed values at an arbitrary point of U, some examples are given in which
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References
Cachafeiro, A. y Marcellán, F. "Orthogonal polynomials and jump modifications". Communication to II International Symposium on Orthogonal Polynomials and their Applications. Segovia, 1986
Freud, G. "Orthogonal Polynomials". Pergamon Press. New York, 1971.
García Lazaro, P. "Modificaciones sobre la función de distribución". Tesina de Licenciatura. U.C. Madrid, 1984.
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© 1988 Springer-Verlag
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Cachafeiro, M.A., Marcellán, F. (1988). Asymptotics for the ratio of the leading coefficients of orthogonal polynomials associated with a jump modification. In: Gómez-Fernandez, J.A., Guerra-Vázquez, F., López-Lagomasino, G., Jiménez-Pozo, M.A. (eds) Approximation and Optimization. Lecture Notes in Mathematics, vol 1354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089587
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DOI: https://doi.org/10.1007/BFb0089587
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50443-6
Online ISBN: 978-3-540-46005-3
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