Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation
In this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [−1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the...
| Main Authors: | , |
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| Format: | Article |
| Language: | Spanish |
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Universidad Industrial de Santander
2015-06-01
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| Series: | Revista Integración |
| Subjects: | |
| Online Access: | http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4770/4929 |
| _version_ | 1819294194471010304 |
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| author | Edinson Fuentes Luis E. Garza |
| author_facet | Edinson Fuentes Luis E. Garza |
| author_sort | Edinson Fuentes |
| collection | DOAJ |
| description | In this paper, we consider perturbations to a sequence of moments
associated with an orthogonality linear functional that is represented by a
positive measure supported in [−1, 1]. In particular, given a perturbation
to such a measure on the real line, we analyze the perturbation obtained
on the corresponding measure on the unit circle, when both measures are
related through the Szeg´´o transformation. A similar perturbation is analyzed
through the inverse Szeg´´o transformation. In both cases, we show that the
applied perturbation can be expressed in terms of the singular part of the
measures, and also in terms of the corresponding sequences of moments.
Resumen. En el presente trabajo, analizamos las perturbaciones a una sucesión
de momentos asociada a un funcional lineal de ortogonalidad que se representa
por una medida positiva con soporte en [−1, 1]. En particular, dada una cierta
perturbación a dicha medida en la recta real, analizamos la perturbación
obtenida en la correspondiente medida en la circunferencia unidad, cuando
dichas medidas están relacionadas por la transformación de Szeg´´o. También
se analiza una perturbación similar a través de la transformación inversa de Szeg´´o. En ambos casos, se muestra que la perturbación aplicada puede ser
expresada en términos de la parte singular de las medidas, y también a través
de las correspondientes sucesiones de momentos. |
| first_indexed | 2024-12-24T04:22:27Z |
| format | Article |
| id | doaj.art-e946e3d7ffcc4411bd7e3f8766510efb |
| institution | Directory Open Access Journal |
| issn | 0120-419X 2145-8472 |
| language | Spanish |
| last_indexed | 2024-12-24T04:22:27Z |
| publishDate | 2015-06-01 |
| publisher | Universidad Industrial de Santander |
| record_format | Article |
| series | Revista Integración |
| spelling | doaj.art-e946e3d7ffcc4411bd7e3f8766510efb2022-12-21T17:15:46ZspaUniversidad Industrial de SantanderRevista Integración0120-419X2145-84722015-06-013316182Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformationEdinson Fuentes0Luis E. Garza1Universidad Pedagógica y Tecnológica de ColombiaUniversidad Nacional de Colombia,Universidad de ColimaIn this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [−1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the corresponding measure on the unit circle, when both measures are related through the Szeg´´o transformation. A similar perturbation is analyzed through the inverse Szeg´´o transformation. In both cases, we show that the applied perturbation can be expressed in terms of the singular part of the measures, and also in terms of the corresponding sequences of moments. Resumen. En el presente trabajo, analizamos las perturbaciones a una sucesión de momentos asociada a un funcional lineal de ortogonalidad que se representa por una medida positiva con soporte en [−1, 1]. En particular, dada una cierta perturbación a dicha medida en la recta real, analizamos la perturbación obtenida en la correspondiente medida en la circunferencia unidad, cuando dichas medidas están relacionadas por la transformación de Szeg´´o. También se analiza una perturbación similar a través de la transformación inversa de Szeg´´o. En ambos casos, se muestra que la perturbación aplicada puede ser expresada en términos de la parte singular de las medidas, y también a través de las correspondientes sucesiones de momentos.http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4770/4929Orthogonal polynomialsStieltjes and Carathéodory functionsHankel and Toeplitz matricesSzeg´´o transformationPolinomios ortogonalesfunciones de Stieltjes y Carathéodorymatrices de Hankel y Toeplitztransformación de Szeg´´o |
| spellingShingle | Edinson Fuentes Luis E. Garza Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation Revista Integración Orthogonal polynomials Stieltjes and Carathéodory functions Hankel and Toeplitz matrices Szeg´´o transformation Polinomios ortogonales funciones de Stieltjes y Carathéodory matrices de Hankel y Toeplitz transformación de Szeg´´o |
| title | Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation |
| title_full | Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation |
| title_fullStr | Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation |
| title_full_unstemmed | Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation |
| title_short | Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation |
| title_sort | analysis of perturbations of moments associated with orthogonality linear functionals through the szego transformation |
| topic | Orthogonal polynomials Stieltjes and Carathéodory functions Hankel and Toeplitz matrices Szeg´´o transformation Polinomios ortogonales funciones de Stieltjes y Carathéodory matrices de Hankel y Toeplitz transformación de Szeg´´o |
| url | http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4770/4929 |
| work_keys_str_mv | AT edinsonfuentes analysisofperturbationsofmomentsassociatedwithorthogonalitylinearfunctionalsthroughtheszegotransformation AT luisegarza analysisofperturbationsofmomentsassociatedwithorthogonalitylinearfunctionalsthroughtheszegotransformation |