{"id":113584,"date":"2018-03-11T10:41:08","date_gmt":"2018-03-11T10:41:08","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/estados-coherentes-generalizados-frames-discretos-y-teoremas-de-reconstruccion\/"},"modified":"2018-03-11T10:41:08","modified_gmt":"2018-03-11T10:41:08","slug":"estados-coherentes-generalizados-frames-discretos-y-teoremas-de-reconstruccion","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/fisica-teorica\/estados-coherentes-generalizados-frames-discretos-y-teoremas-de-reconstruccion\/","title":{"rendered":"Estados coherentes generalizados, frames discretos y teoremas de reconstrucci\u00f3n"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Juan  Carlos Sanchez Monreal <\/strong><\/h2>\n<p>Resumen  usando t\u00e9cnicas de estados coherentes, probamos teoremas de muestreo para funciones holomorfas sobre la esfera de riemann, el hiperboloide y el plano complejo, vistos como espacios homog\u00e9neos de los grupos  su(2), su(1,1) y de  heisenberg-weyl, respectivamente. Proporcionamos f\u00f3rmulas de reconstrucci\u00f3n como una convoluci\u00f3n de n muestras (las ra\u00edces n-\u00e9simas de la unidad) con un n\u00facleo de reconstrucci\u00f3n (de tipo sinc) y obtenemos transformadas de fourier discretas, lo que permite f\u00f3rmulas de inversi\u00f3n para los operadores resoluci\u00f3n y kernel de solapamiento haciendo uso de la teor\u00eda de matrices circulantes y de matrices rectangulares de fourier.  Para el caso del  hiperpoloide y el plano complejo, discutimos tambi\u00e9n el efecto de submuestreo, introduciendo el concepto de &quot;pseudo-frame&quot;, y las condiciones bajo las cuales es posible una reconstrucci\u00f3n parcial a partir de n muestras, as\u00ed  como la precisi\u00f3n de tal aproximaci\u00f3n, que tiende a ser exacta cuando n tiende a infinito.   palabras clave  estados coherentes, grupos de lie, funciones holomorfas, muestreo, frames discretos, teoremas de reconstrucci\u00f3n,  nyquist-shannon, aproximaci\u00f3n, transformada de fourier discreta.  abstract   using coherent-state techniques, we prove sampling theorems for holomorphic functions on the riemann sphere, the hyperboloid (lobachevski plane)  and the complex plane, seen as homogeneous spaces of the unitary su(2), pseudo-unitary su(1,1) and heisenberg-weyl groups, respectively. We provide reconstruction formulas as a convolution product of n samples (the nth-roots of unity) and a given reconstruction kernel (a sinc-type function) and obtain discrete fourier transforms from these n samples, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of circulant matrices and rectangular fourier matrices.  For the hyperboloid and complex plane, we also discuss the effect of  under-sampling, introducing the concept of  &quot;pseudo-frame&quot;,  and the conditions under which a partial reconstruction from n samples is still possible and the accuracy of the approximation, which tends to be exact in the limit when n  tends to infinity.     keywords   coherent states, lie groups, holomorphic functions,  sampling, dicrete frames, reconstruction  theorems,  nyquist-shannon, approximation, discrete fourier transform.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Estados coherentes generalizados, frames discretos y teoremas de reconstrucci\u00f3n<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Estados coherentes generalizados, frames discretos y teoremas de reconstrucci\u00f3n <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Juan  Carlos Sanchez Monreal <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Murcia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 14\/12\/2012<\/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>Manuel Calixto Molina<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: victor Aldaya valverde <\/li>\n<li>sergio Amat plata (vocal)<\/li>\n<li>domingo Barrera rosillo (vocal)<\/li>\n<li>Mar\u00eda Moncayo hormigo (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Juan Carlos Sanchez Monreal Resumen usando t\u00e9cnicas de estados coherentes, probamos teoremas de muestreo para funciones holomorfas [&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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