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Please use this identifier to cite or link to this item: http://hdl.handle.net/10481/32692

Title: Continuous symmetrized Sobolev inner products of order N (II)
Authors: Bueno, María Isabel
Marcellán Español, Francisco
Sánchez-Ruiz, Jorge
Issue Date: 2006
Abstract: Given a symmetrized Sobolev inner product of order N, the corresponding sequence of monic orthogonal polynomials {Qn} satisfies Q2n(x)=Pn(x2), Q2n+1(x)=xRn(x2) for certain sequences of monic polynomials {Pn} and {Rn}. In this paper we consider the particular case when all the measures that define the symmetrized Sobolev inner product are equal, absolutely continuous and semiclassical. Under such restrictions, we give explicit algebraic relations between the sequences {Pn} and {Rn}, as well as higher-order recurrence relations that they satisfy.
Sponsorship: The work of the authors has been partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grants BFM 2003-06335-C03-02 (M.I.B., F.M., J.S.R.) and BFM2001-3878-C02-01 (J.S.R.), INTAS Research Network NeCCA INTAS 03-51-6637 (F.M.), and the Junta de Andalucía research group FQM-0207 (J.S.R).
Publisher: Kent State University. Institute of Computational Mathematics
Keywords: Sobolev inner product
Orthogonal polynomials
Semiclassical linear functionals
Recurrence relation
Symmetrization process
URI: http://hdl.handle.net/10481/32692
ISSN: 1068-9613
Rights : Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License
Citation: Bueno, M.I.; Marcellán, F.; Sánchez-Ruiz, J. Continuous symmetrized Sobolev inner products of order N (II). Electronic Transactions on Numerical Analysis (ETNA), 24: 55-65 (2006). [http://hdl.handle.net/10481/32692]
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