Multivariate Orthogonal Polynomials and Modified Moment Functionals
Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass poin...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147849 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Multivariate Orthogonal Polynomials and Modified Moment Functionals / A.M. Delgado, L. Fernández, T.E. Pérez, M.A. Piñar // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718868856766464 |
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| author | Delgado, A.M. Fernández, L. Pérez, T.E. Piñar, M.A. |
| author_facet | Delgado, A.M. Fernández, L. Pérez, T.E. Piñar, M.A. |
| citation_txt | Multivariate Orthogonal Polynomials and Modified Moment Functionals / A.M. Delgado, L. Fernández, T.E. Pérez, M.A. Piñar // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass points, or by multiplying it times a polynomial of total degree 2, respectively. Orthogonal polynomials associated with modified moment functionals will be studied, as well as the impact of the modification in useful properties of the orthogonal polynomials. Finally, some illustrative examples will be given.
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| first_indexed | 2025-12-07T18:17:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147849 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:17:49Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Delgado, A.M. Fernández, L. Pérez, T.E. Piñar, M.A. 2019-02-16T09:16:25Z 2019-02-16T09:16:25Z 2016 Multivariate Orthogonal Polynomials and Modified Moment Functionals / A.M. Delgado, L. Fernández, T.E. Pérez, M.A. Piñar // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C50; 42C10 DOI:10.3842/SIGMA.2016.090 https://nasplib.isofts.kiev.ua/handle/123456789/147849 Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass points, or by multiplying it times a polynomial of total degree 2, respectively. Orthogonal polynomials associated with modified moment functionals will be studied, as well as the impact of the modification in useful properties of the orthogonal polynomials. Finally, some illustrative examples will be given. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
 The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
 
 The authors are really grateful to the anonymous referees for their valuable suggestions and comments
 which led us to improve this paper. This work has been partially supported by MINECO
 of Spain and the European Regional Development Fund (ERDF) through grant MTM2014–
 53171–P, and Junta de Andaluc´ıa grant P11–FQM–7276 and research group FQM–384. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multivariate Orthogonal Polynomials and Modified Moment Functionals Article published earlier |
| spellingShingle | Multivariate Orthogonal Polynomials and Modified Moment Functionals Delgado, A.M. Fernández, L. Pérez, T.E. Piñar, M.A. |
| title | Multivariate Orthogonal Polynomials and Modified Moment Functionals |
| title_full | Multivariate Orthogonal Polynomials and Modified Moment Functionals |
| title_fullStr | Multivariate Orthogonal Polynomials and Modified Moment Functionals |
| title_full_unstemmed | Multivariate Orthogonal Polynomials and Modified Moment Functionals |
| title_short | Multivariate Orthogonal Polynomials and Modified Moment Functionals |
| title_sort | multivariate orthogonal polynomials and modified moment functionals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147849 |
| work_keys_str_mv | AT delgadoam multivariateorthogonalpolynomialsandmodifiedmomentfunctionals AT fernandezl multivariateorthogonalpolynomialsandmodifiedmomentfunctionals AT perezte multivariateorthogonalpolynomialsandmodifiedmomentfunctionals AT pinarma multivariateorthogonalpolynomialsandmodifiedmomentfunctionals |