{"id":145490,"date":"1993-01-01T00:00:00","date_gmt":"1993-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sobre-la-ecuacion-funcional-de-cauchy-y-generalizaciones-de-esta-en-dominios-numericos-restringidos\/"},"modified":"1993-01-01T00:00:00","modified_gmt":"1993-01-01T00:00:00","slug":"sobre-la-ecuacion-funcional-de-cauchy-y-generalizaciones-de-esta-en-dominios-numericos-restringidos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/sobre-la-ecuacion-funcional-de-cauchy-y-generalizaciones-de-esta-en-dominios-numericos-restringidos\/","title":{"rendered":"Sobre la ecuacion funcional de cauchy y generalizaciones de esta en dominios numericos restringidos."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jes\u00fas Salillas Cantarelo <\/strong><\/h2>\n<p>Se han desarrollado multitud de modelos funcionales basados en las tecnicas introducidas por j. Aczel sobre ecuaciones funcionales en los que destaca la ecuacion funcional de cauchy, f(x+y)=f(x)+f(y). Las representaciones funcionales que aparecen en los modelos, sometidas a las restricciones de esta, conducen a ecuaciones funcionales de cauchy condicionadas o en dominios restringidos. La tesis consiste en un estudio sistematico de ecuaciones funcionales involucrando cuadrados.  el capitulo 1 trata de la ecuacion funcional f(x2+y)=f(x2)+f(y) en algunos anillos y se demuestra que no siempre equivale a la de cauchy. En el 2 se demuestra la equiValencia de ambas ecuaciones en los cuerpos finitos fq con q=pn (p primo), en q y q(alfa), alfa algebraico. El 3 versa sobre la ecuacion funcional f(x2+y2)=f(x)2+f(y)2 en n0, z, q, z(i), q(i) obteniendo siempre las soluciones de la misma. En el 4 se obtienen como soluciones (no triviales) de esta ecuacion en los cuerpos finitos: el automorfismo de frobenius y sus potencias. El 5 relaciona la ecuacion funcional anterior con las funcionales cuadraticas resolviendola en los cuerpos de numeros que contienen raiz cuadrada 2.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sobre la ecuacion funcional de cauchy y generalizaciones de esta en dominios numericos restringidos.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sobre la ecuacion funcional de cauchy y generalizaciones de esta en dominios numericos restringidos. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jes\u00fas Salillas Cantarelo <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1993<\/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> Garcia Roig Jaime Luis<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Enrique Trillas Ruiz <\/li>\n<li>Josep Rifa Coma (vocal)<\/li>\n<li>Claudi Alsina Catala (vocal)<\/li>\n<li> Laita De La Riba Luis (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jes\u00fas Salillas Cantarelo Se han desarrollado multitud de modelos funcionales basados en las tecnicas introducidas por j. [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[3183,15084,126,15596],"tags":[3602,3601,35087,35090,12503,260445],"class_list":["post-145490","post","type-post","status-publish","format-standard","hentry","category-analisis-y-analisis-funcional","category-ecuaciones-funcionales","category-matematicas","category-politecnica-de-catalunya","tag-claudi-alsina-catala","tag-enrique-trillas-ruiz","tag-garcia-roig-jaime-luis","tag-jesus-salillas-cantarelo","tag-josep-rifa-coma","tag-laita-de-la-riba-luis"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/145490","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=145490"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/145490\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=145490"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=145490"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=145490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}