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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/5946
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| Title: | Continuous symmetrized Sobolev inner products of order N (I) |
| Author(s): | Bueno, M. Isabel
Marcellán, Francisco
Sánchez-Ruiz, Jorge |
| Publisher: | Elsevier |
| Issued date: | 1-Jun-2005 |
| Citation: | Journal of Mathematical Analysis and Applications, 2005, vol. 306, n. 1, p. 83-96 |
| URI: | http://hdl.handle.net/10016/5946 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2004.11.052 |
| Description: | 14 pages, no figures.-- MSC2000 codes: 42C05
MR#: MR2132890 (2005k:42068)
Zbl#: Zbl 1076.42017 |
| Abstract: | Given a symmetrized Sobolev inner product of order N, the corresponding sequence of monic orthogonal polynomials {Qn} satisfies that Q_2n(x)=Pn(x2), Q_2n+1(x)=xRn(x2) for certain sequences of monic polynomials {Pn} and {Rn}. In this paper, we deduce the integral representation of the inner products such that {Pn} and {Rn} are the corresponding sequences of orthogonal polynomials. Moreover, we state a relation between both inner products which extends the classical result for symmetric linear functionals. |
| Sponsor: | 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.), NATO collaborative grant PST.CLG.979738 (M.I.B., F.M.), and the Junta de Andalucía research group FQM-0207 (J.S.R). |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1016/j.jmaa.2004.11.052 |
| Keywords: | Sobolev inner product
Orthogonal polynomials
Symmetrization process |
| Rights: | © Elsevier |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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