Commutators on Fock spaces

Detalhes bibliográficos
Autor(a) principal: Alpay, Daniel
Data de Publicação: 2023
Outros Autores: Cerejeiras, Paula, Kähler, Uwe, Kling, Trevor
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/37009
Resumo: Given a weighted l2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond–Leontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic Weyl–Heisenberg algebra. Concrete examples for its application are provided.
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spelling Commutators on Fock spacesFock spaceCommutatorsGelfond–Leontiev derivativesGiven a weighted l2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond–Leontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic Weyl–Heisenberg algebra. Concrete examples for its application are provided.AIP Publishing2024-04-03T00:00:00Z2023-04-03T00:00:00Z2023-04-03info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/37009eng0022-248810.1063/5.0080723Alpay, DanielCerejeiras, PaulaKähler, UweKling, Trevorinfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:10:58Zoai:ria.ua.pt:10773/37009Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:07:30.820330Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Commutators on Fock spaces
title Commutators on Fock spaces
spellingShingle Commutators on Fock spaces
Alpay, Daniel
Fock space
Commutators
Gelfond–Leontiev derivatives
title_short Commutators on Fock spaces
title_full Commutators on Fock spaces
title_fullStr Commutators on Fock spaces
title_full_unstemmed Commutators on Fock spaces
title_sort Commutators on Fock spaces
author Alpay, Daniel
author_facet Alpay, Daniel
Cerejeiras, Paula
Kähler, Uwe
Kling, Trevor
author_role author
author2 Cerejeiras, Paula
Kähler, Uwe
Kling, Trevor
author2_role author
author
author
dc.contributor.author.fl_str_mv Alpay, Daniel
Cerejeiras, Paula
Kähler, Uwe
Kling, Trevor
dc.subject.por.fl_str_mv Fock space
Commutators
Gelfond–Leontiev derivatives
topic Fock space
Commutators
Gelfond–Leontiev derivatives
description Given a weighted l2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond–Leontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic Weyl–Heisenberg algebra. Concrete examples for its application are provided.
publishDate 2023
dc.date.none.fl_str_mv 2023-04-03T00:00:00Z
2023-04-03
2024-04-03T00:00:00Z
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://hdl.handle.net/10773/37009
url http://hdl.handle.net/10773/37009
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-2488
10.1063/5.0080723
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv AIP Publishing
publisher.none.fl_str_mv AIP Publishing
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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