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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/5900
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| Title: | When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials? |
| Author(s): | Alfaro, Manuel
Marcellán, Francisco
Peña, Ana
Rezola, M. Luisa |
| Publisher: | Elsevier |
| Issued date: | Jan-2010 |
| Citation: | Journal of Computational and Applied Mathematics, 2010, vol. 233, n. 6, p. 1446-1452 |
| URI: | http://hdl.handle.net/10016/5900 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2009.02.060 |
| Description: | 7 pages, no figures.-- MSC2000 codes: 33C45; 42C05.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics" (Special issue dedicated to Professor Jesús Sánchez Dehesa on the occasion of his 60th birthday). |
| Abstract: | Given {Pn}n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e.,
Qn(x) = Pn(x) + a1Pn-1(x) + ... + akPn-k(x), ak<>0, n>k.
Necessary and sufficient conditions are given for the orthogonality of the sequence {Qn}n≥0. An interesting interpretation in terms of the Jacobi matrices associated with {Pn}n≥0 and {Qn}n≥0 is shown. |
| Sponsor: | MA and MLR partially supported by Ministerio de Educación y Ciencia (MEC) of Spain under Grant MTM 2006-13000-C03-03 and Diputación General de Aragón (DGA) project E-64. FM partially supported by MEC of Spain under Grant MTM 2006-13000-C03-02 and INTAS Research Network NeCCA 03-51-6637. AP partially supported by MEC of Spain under Grants MTM 2004-03036 and MTM 2006-13000-C03-03 and DGA project E-64. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1016/j.cam.2009.02.060 |
| Keywords: | Orthogonal polynomials
Recurrence relations
Linear functionals
Chebyshev polynomials
Difference equations |
| Rights: | © Elsevier |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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