{"id":93718,"date":"2009-03-06T00:00:00","date_gmt":"2009-03-06T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/asymptotic-properties-of-mixed-type-multiple-ortogonal-polynomials-for-nikishin-systems\/"},"modified":"2009-03-06T00:00:00","modified_gmt":"2009-03-06T00:00:00","slug":"asymptotic-properties-of-mixed-type-multiple-ortogonal-polynomials-for-nikishin-systems","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/teoria-de-la-aproximacion\/asymptotic-properties-of-mixed-type-multiple-ortogonal-polynomials-for-nikishin-systems\/","title":{"rendered":"Asymptotic properties of mixed type multiple ortogonal polynomials for nikishin systems"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Abey Lopez Garcia <\/strong><\/h2>\n<p>Se estudian tres tipos de relaciones  asint\u00f3ticas que satisfacen familias de polinomios ortogonales  m\u00faltiples con respecto a sistemas de medidas de nikishin.  las familias de polinomios de ortogonalidad m\u00faltiple son aquellos en que los polinomios satisfacen relaciones de ortogonalidad compartidas entre varias medidas. El grado de ortogonalidad respecto a cada medida se controla a partir de un multi-indice.  los sistemas de nikishin son familias finitas de medidas que se construyen de manera recurrente siguiendo un cierto patr\u00f3n. Tales sistemas fueron introducidos por nikishin en el a\u00f1o 1980. Su importancia radica, entre otros motivos, a que tales sistemas resultan apropiados para extender varias aplicaciones importantes de la teor\u00eda de polinomios ortogonales: a la aproximaci\u00f3n simultanea de funciones anal\u00edticas, al desarrollo de formulas de cuadratura simultanea de tipo gauss-jacobi, en la teor\u00eda de n\u00fameros, en el estudio de matrices aleatorias y movimientos brownianes de trayectorias que no se intersectan.  para la demostraci\u00f3n de la convergencia de tales procedimientos y\/o el estudio de sus propiedades es necesario tener estimaciones del comportamiento asint\u00f3tico de los polinomios de ortogonalidad mixtos asociados al sistema de medidas, en particular, el comportamiento de la ra\u00edz en\u00e9sima (donde n es la suma de las componentes del multi-\u00edndice), la del cociente de polinomios consecutivos y la relativa entre dos familias de polinomios de ortogonalidad m\u00faltiples donde la segunda familia se obtiene a partir de una perturbaci\u00f3n de las medidas a las cuales est\u00e1n asociados los polinomios de la primera. Estos tres tipos de propiedades asint\u00f3ticas se estudian en la tesis y se dan f\u00f3rmulas para los l\u00edmites.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Asymptotic properties of mixed type multiple ortogonal polynomials for nikishin systems<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Asymptotic properties of mixed type multiple ortogonal polynomials for nikishin systems <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Abey Lopez Garcia <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Carlos III de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 03\/06\/2009<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Guillermo Lopez Lagomasino<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Francisco Marcellan espa\u00f1ol <\/li>\n<li>arnoldus Kuijlaars (vocal)<\/li>\n<li>andrei Mart\u00ednez finkelshtein (vocal)<\/li>\n<li>alexander Aptekarev (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Abey Lopez Garcia Se estudian tres tipos de relaciones asint\u00f3ticas que satisfacen familias de polinomios ortogonales m\u00faltiples [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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