Extensiones matriciales de polinomios ortogonales
Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación, 2024.
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| Format: | doctoralThesis biblioteca |
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2024-03-25
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| Subjects: | Polinomios ortogonales matriciales, Medidas discretas, Funciones hipergeométricas, Ecuaciones de Toda, Par de Lax, Polinomios excepcionales, Polinomios duales, Matrix orthogonal polynomials, Discrete measures, Hypergeometric functions, Toda equations, Lax pair, Exceptional polynomials, Dual polynomials, Orthogonal polynomials and functions of hypergeometric type, Other special orthogonal polynomials and functions, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, Orthogonal functions and polynomials, |
| Online Access: | http://hdl.handle.net/11086/551442 |
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dig-unc-ar-11086-5514422024-04-17T06:37:48Z Extensiones matriciales de polinomios ortogonales Morey, Lucía Román, Pablo Manuel Polinomios ortogonales matriciales Medidas discretas Funciones hipergeométricas Ecuaciones de Toda Par de Lax Polinomios excepcionales Polinomios duales Matrix orthogonal polynomials Discrete measures Hypergeometric functions Toda equations Lax pair Exceptional polynomials Dual polynomials Orthogonal polynomials and functions of hypergeometric type Other special orthogonal polynomials and functions Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems Orthogonal functions and polynomials Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación, 2024. Fil: Morey, Lucía. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. La teoría de polinomios ortogonales matriciales fue introducida por Krein en la década de 1940 y, desde entonces, ha sido estudiada en distintos contextos. En este trabajo, nos enfocaremos en el estudio de propiedades de polinomios ortogonales matriciales en la recta real. Nuestro interés radica en la exploración de extensiones matriciales de polinomios ortogonales escalares, así como también de sus propiedades destacadas. Esta tesis está estructurada en tres partes independientes. Cada una de estas partes se dedica al estudio de una extensión matricial diferente de polinomios ortogonales escalares. En la primer parte estudiamos una noción de dualidad para polinomios ortogonales en los enteros no negativos. En la segunda parte estudiamos polinomios excepcionales matriciales. En la última parte estudiamos ecuaciones no abelianas de tipo Toda. The theory of matrix-valued orthogonal polynomials was introduced by Krein in the 1940’s and, since then, has been studied in different contexts. In this work, we will focus on studying properties of matrix orthogonal polynomials on the real line. Our interest lies in exploring matrix extensions of scalar orthogonal polynomials, as well as their prominent properties. This thesis is structured into three independent parts. Each of these parts is devoted to the study of a different matrix extension of scalar orthogonal polynomials. In the first part we study a notion of duality for matrix valued orthogonal polynomials on the non negative integers. In the second part we study matrix valued exceptional polynomials. In the last part we study non-Abelian Toda type equations. Fil: Morey, Lucía. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. 2024-04-16T16:14:43Z 2024-04-16T16:14:43Z 2024-03-25 doctoralThesis http://hdl.handle.net/11086/551442 spa Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ |
| institution |
UNC AR |
| collection |
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| country |
Argentina |
| countrycode |
AR |
| component |
Bibliográfico |
| access |
En linea |
| databasecode |
dig-unc-ar |
| tag |
biblioteca |
| region |
America del Sur |
| libraryname |
Biblioteca 'Ing. Agrónomo Moisés Farber' de la Facultad de Ciencias Agropecuarias |
| language |
spa |
| topic |
Polinomios ortogonales matriciales Medidas discretas Funciones hipergeométricas Ecuaciones de Toda Par de Lax Polinomios excepcionales Polinomios duales Matrix orthogonal polynomials Discrete measures Hypergeometric functions Toda equations Lax pair Exceptional polynomials Dual polynomials Orthogonal polynomials and functions of hypergeometric type Other special orthogonal polynomials and functions Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems Orthogonal functions and polynomials Polinomios ortogonales matriciales Medidas discretas Funciones hipergeométricas Ecuaciones de Toda Par de Lax Polinomios excepcionales Polinomios duales Matrix orthogonal polynomials Discrete measures Hypergeometric functions Toda equations Lax pair Exceptional polynomials Dual polynomials Orthogonal polynomials and functions of hypergeometric type Other special orthogonal polynomials and functions Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems Orthogonal functions and polynomials |
| spellingShingle |
Polinomios ortogonales matriciales Medidas discretas Funciones hipergeométricas Ecuaciones de Toda Par de Lax Polinomios excepcionales Polinomios duales Matrix orthogonal polynomials Discrete measures Hypergeometric functions Toda equations Lax pair Exceptional polynomials Dual polynomials Orthogonal polynomials and functions of hypergeometric type Other special orthogonal polynomials and functions Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems Orthogonal functions and polynomials Polinomios ortogonales matriciales Medidas discretas Funciones hipergeométricas Ecuaciones de Toda Par de Lax Polinomios excepcionales Polinomios duales Matrix orthogonal polynomials Discrete measures Hypergeometric functions Toda equations Lax pair Exceptional polynomials Dual polynomials Orthogonal polynomials and functions of hypergeometric type Other special orthogonal polynomials and functions Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems Orthogonal functions and polynomials Morey, Lucía Extensiones matriciales de polinomios ortogonales |
| description |
Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación, 2024. |
| author2 |
Román, Pablo Manuel |
| author_facet |
Román, Pablo Manuel Morey, Lucía |
| format |
doctoralThesis |
| topic_facet |
Polinomios ortogonales matriciales Medidas discretas Funciones hipergeométricas Ecuaciones de Toda Par de Lax Polinomios excepcionales Polinomios duales Matrix orthogonal polynomials Discrete measures Hypergeometric functions Toda equations Lax pair Exceptional polynomials Dual polynomials Orthogonal polynomials and functions of hypergeometric type Other special orthogonal polynomials and functions Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems Orthogonal functions and polynomials |
| author |
Morey, Lucía |
| author_sort |
Morey, Lucía |
| title |
Extensiones matriciales de polinomios ortogonales |
| title_short |
Extensiones matriciales de polinomios ortogonales |
| title_full |
Extensiones matriciales de polinomios ortogonales |
| title_fullStr |
Extensiones matriciales de polinomios ortogonales |
| title_full_unstemmed |
Extensiones matriciales de polinomios ortogonales |
| title_sort |
extensiones matriciales de polinomios ortogonales |
| publishDate |
2024-03-25 |
| url |
http://hdl.handle.net/11086/551442 |
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AT moreylucia extensionesmatricialesdepolinomiosortogonales |
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