On close to scalar families for fractional evolution equations: zero–one law
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s00233-019-10025-0 http://hdl.handle.net/11449/189151 |
Resumo: | For {Rα,β(t)}t≥0 being a strongly continuous (α, β) -resolvent family on a Banach space, we show that the assumption supt>0‖1tβ-1Eα,β(λtα)Rα,β(t)-I‖=:θ<1 yields that Rα , β(t) = tβ - 1Eα , β(λtα) for all t> 0 and λ≥ 0 , where Eα , β(s) denotes the Mittag–Leffler function with parameters α, β> 0. This implication is known as the zero–one law. In particular, we provide new insights on the structural properties of the theories of C-semigroups, strongly continuous cosine families, β-times integrated semigroups and α-resolvent families, among others. For β-times integrated semigroups, an example shows that in the sector {(α,β):0<α≤1;α≤β} the requirement θ< 1 is optimal: for θ= 1 the result is false. |
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Repositório Institucional da UNESP |
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On close to scalar families for fractional evolution equations: zero–one lawC-semigroupsCosine familiesOne parameter families of bounded operatorsOne–zero lawα-resolvent familiesβ-times integratedFor {Rα,β(t)}t≥0 being a strongly continuous (α, β) -resolvent family on a Banach space, we show that the assumption supt>0‖1tβ-1Eα,β(λtα)Rα,β(t)-I‖=:θ<1 yields that Rα , β(t) = tβ - 1Eα , β(λtα) for all t> 0 and λ≥ 0 , where Eα , β(s) denotes the Mittag–Leffler function with parameters α, β> 0. This implication is known as the zero–one law. In particular, we provide new insights on the structural properties of the theories of C-semigroups, strongly continuous cosine families, β-times integrated semigroups and α-resolvent families, among others. For β-times integrated semigroups, an example shows that in the sector {(α,β):0<α≤1;α≤β} the requirement θ< 1 is optimal: for θ= 1 the result is false.Departamento de Matemática Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp), R. Cristóvâo Colombo, 2265 - Jardim NazarethDepartamento de Matemática y Ciencia de la Computación Facultad de Ciencias Universidad de Santiago de Chile (Usach), Las Sophoras 173, Estación CentralDepartamento de Matemática Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp), R. Cristóvâo Colombo, 2265 - Jardim NazarethUniversidade Estadual Paulista (Unesp)Universidad de Santiago de Chile (Usach)Gambera, Laura R. [UNESP]Lizama, CarlosProkopczyk, Andrea [UNESP]2019-10-06T16:31:26Z2019-10-06T16:31:26Z2019-08-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article140-152http://dx.doi.org/10.1007/s00233-019-10025-0Semigroup Forum, v. 99, n. 1, p. 140-152, 2019.0037-1912http://hdl.handle.net/11449/18915110.1007/s00233-019-10025-02-s2.0-85066018146Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSemigroup Foruminfo:eu-repo/semantics/openAccess2021-10-23T19:23:36Zoai:repositorio.unesp.br:11449/189151Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:05:07.638326Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
On close to scalar families for fractional evolution equations: zero–one law |
title |
On close to scalar families for fractional evolution equations: zero–one law |
spellingShingle |
On close to scalar families for fractional evolution equations: zero–one law Gambera, Laura R. [UNESP] C-semigroups Cosine families One parameter families of bounded operators One–zero law α-resolvent families β-times integrated |
title_short |
On close to scalar families for fractional evolution equations: zero–one law |
title_full |
On close to scalar families for fractional evolution equations: zero–one law |
title_fullStr |
On close to scalar families for fractional evolution equations: zero–one law |
title_full_unstemmed |
On close to scalar families for fractional evolution equations: zero–one law |
title_sort |
On close to scalar families for fractional evolution equations: zero–one law |
author |
Gambera, Laura R. [UNESP] |
author_facet |
Gambera, Laura R. [UNESP] Lizama, Carlos Prokopczyk, Andrea [UNESP] |
author_role |
author |
author2 |
Lizama, Carlos Prokopczyk, Andrea [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidad de Santiago de Chile (Usach) |
dc.contributor.author.fl_str_mv |
Gambera, Laura R. [UNESP] Lizama, Carlos Prokopczyk, Andrea [UNESP] |
dc.subject.por.fl_str_mv |
C-semigroups Cosine families One parameter families of bounded operators One–zero law α-resolvent families β-times integrated |
topic |
C-semigroups Cosine families One parameter families of bounded operators One–zero law α-resolvent families β-times integrated |
description |
For {Rα,β(t)}t≥0 being a strongly continuous (α, β) -resolvent family on a Banach space, we show that the assumption supt>0‖1tβ-1Eα,β(λtα)Rα,β(t)-I‖=:θ<1 yields that Rα , β(t) = tβ - 1Eα , β(λtα) for all t> 0 and λ≥ 0 , where Eα , β(s) denotes the Mittag–Leffler function with parameters α, β> 0. This implication is known as the zero–one law. In particular, we provide new insights on the structural properties of the theories of C-semigroups, strongly continuous cosine families, β-times integrated semigroups and α-resolvent families, among others. For β-times integrated semigroups, an example shows that in the sector {(α,β):0<α≤1;α≤β} the requirement θ< 1 is optimal: for θ= 1 the result is false. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-06T16:31:26Z 2019-10-06T16:31:26Z 2019-08-15 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s00233-019-10025-0 Semigroup Forum, v. 99, n. 1, p. 140-152, 2019. 0037-1912 http://hdl.handle.net/11449/189151 10.1007/s00233-019-10025-0 2-s2.0-85066018146 |
url |
http://dx.doi.org/10.1007/s00233-019-10025-0 http://hdl.handle.net/11449/189151 |
identifier_str_mv |
Semigroup Forum, v. 99, n. 1, p. 140-152, 2019. 0037-1912 10.1007/s00233-019-10025-0 2-s2.0-85066018146 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Semigroup Forum |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
140-152 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128456983052288 |