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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/5991
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| Title: | Lebesgue perturbation of a quasi-definite Hermitian functional. The positive definite case |
| Author(s): | Cachafeiro, Alicia
Marcellán, Francisco
Pérez, C. |
| Publisher: | Elsevier |
| Issued date: | 1-Aug-2003 |
| Citation: | Linear Algebra and its Applications, 2003, vol. 369, p. 235-250 |
| URI: | http://hdl.handle.net/10016/5991 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/S0024-3795(02)00728-0 |
| Description: | 16 pages, no figures.-- MSC2000 codes: 33C47; 42C05.
MR#: MR1988489 (2004d:42042)
Zbl#: Zbl 1032.42030 |
| Abstract: | In this work we study the problem of orthogonality with respect to a sum of measures or functionals. First we consider the case where one of the functionals is arbitrary and quasi-definite and the other one is the Lebesgue normalized functional. Next we study the sum of two positive measures. The first one is arbitrary and the second one is the Lebesgue normalized measure and we obtain some relevant properties concerning the new measure. Finally we consider the sum of a Bernstein–Szegö measure and the Lebesgue measure. In this case we obtain more simple explicit algebraic relations as well as the relation between the corresponding Szegö’s functions. |
| Sponsor: | First (A.C.) and third (C.P.) author's research was supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant number BFM2000-0015 and by Universidad de Vigo and Xunta de Galicia. Second author (F.M.)'s research was supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM2000-0206-C04-01 and INTAS project INTAS2000-272. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1016/S0024-3795(02)00728-0 |
| Keywords: | Orthogonal polynomials
Quasi-definite functionals
Lebesgue measure
Szegö condition
Bernstein–Szegö measures |
| Rights: | © Elsevier |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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