Cosine families of operators in a class of Fréchet spaces

Abstract: M. sova ((10)) proved that the infinitesimal generator of all uniformly continuous cosine family, of operators in Banach space, is a bounded operator. We show by counter-example that the result mentioned above is not true in general on Fréchet spaces, and we prove that the infinitesimal ge...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Hassani,Rachid Ameziane, Blali,Aziz, Amrani,Abdelkhalek El, Moussaouja,Khalil
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:	Strongly continuous cosine families Semi-groups of operators Locally convex space Quojection Fréchet space
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100103
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172018000100103
record_format	dspace
spelling	oai:scielo:S0716-091720180001001032018-03-13Cosine families of operators in a class of Fréchet spacesHassani,Rachid AmezianeBlali,AzizAmrani,Abdelkhalek ElMoussaouja,Khalil Strongly continuous cosine families Semi-groups of operators Locally convex space Quojection Fréchet space Abstract: M. sova ((10)) proved that the infinitesimal generator of all uniformly continuous cosine family, of operators in Banach space, is a bounded operator. We show by counter-example that the result mentioned above is not true in general on Fréchet spaces, and we prove that the infinitesimal generator of an uniformly continuous cosine family of operators in a class of Fréchet spaces (quojection) is necessarily continuous.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.1 20182018-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100103en10.4067/S0716-09172018000100103
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Strongly continuous cosine families Semi-groups of operators Locally convex space Quojection Fréchet space
spellingShingle	Strongly continuous cosine families Semi-groups of operators Locally convex space Quojection Fréchet space Hassani,Rachid Ameziane Blali,Aziz Amrani,Abdelkhalek El Moussaouja,Khalil Cosine families of operators in a class of Fréchet spaces
description	Abstract: M. sova ((10)) proved that the infinitesimal generator of all uniformly continuous cosine family, of operators in Banach space, is a bounded operator. We show by counter-example that the result mentioned above is not true in general on Fréchet spaces, and we prove that the infinitesimal generator of an uniformly continuous cosine family of operators in a class of Fréchet spaces (quojection) is necessarily continuous.
author	Hassani,Rachid Ameziane Blali,Aziz Amrani,Abdelkhalek El Moussaouja,Khalil
author_facet	Hassani,Rachid Ameziane Blali,Aziz Amrani,Abdelkhalek El Moussaouja,Khalil
author_sort	Hassani,Rachid Ameziane
title	Cosine families of operators in a class of Fréchet spaces
title_short	Cosine families of operators in a class of Fréchet spaces
title_full	Cosine families of operators in a class of Fréchet spaces
title_fullStr	Cosine families of operators in a class of Fréchet spaces
title_full_unstemmed	Cosine families of operators in a class of Fréchet spaces
title_sort	cosine families of operators in a class of fréchet spaces
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100103
work_keys_str_mv	AT hassanirachidameziane cosinefamiliesofoperatorsinaclassoffrechetspaces AT blaliaziz cosinefamiliesofoperatorsinaclassoffrechetspaces AT amraniabdelkhalekel cosinefamiliesofoperatorsinaclassoffrechetspaces AT moussaoujakhalil cosinefamiliesofoperatorsinaclassoffrechetspaces
_version_	1718439832211947520

Cosine families of operators in a class of Fréchet spaces

Ejemplares similares