Publicação
On fractional semidiscrete Dirac operators of Lévy-Leblond type
| Resumo: | In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L\'evy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z}^n\times[0,\infty)$ ($h>0$), resembling to fractional semidiscrete counterparts of the so-called parabolic Dirac operators. The methods adopted here are fairly operational, relying mostly on the algebraic manipulations involving Clifford algebras, discrete Fourier analysis techniques as well as standard properties of the analytic fractional semidiscrete semigroup $\left\{\exp(-te^{i\theta}(-\Delta_h)^{\alpha})\right\}_{t\geq 0}$, carrying the parameter constraints $0<\alpha\leq 1$ and $|\theta|\leq \frac{\alpha \pi}{2}$. The results obtained involve the study of Cauchy problems on $h\mathbb{Z}^n\times[0,\infty)$. |
|---|---|
| Autores principais: | Faustino, Nelson |
| Assunto: | Fractional semidiscrete Dirac operators Riemann–Liouville fractional derivative Fractional discrete Laplacian |
| Ano: | 2023 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Aveiro |
| Idioma: | inglês |
| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
| _version_ | 1866173158548045824 |
|---|---|
| author | Faustino, Nelson |
| author_facet | Faustino, Nelson |
| author_role | author |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Faustino, Nelson\"}] |
| datacite.creators.creator.creatorName.fl_str_mv | Faustino, Nelson |
| datacite.date.Accepted.fl_str_mv | 2023-07-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2023-10-10T10:37:57Z |
| datacite.date.embargoed.fl_str_mv | 2023-10-10T10:37:57Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Fractional semidiscrete Dirac operators Riemann–Liouville fractional derivative Fractional discrete Laplacian |
| datacite.titles.title.fl_str_mv | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| dc.creator.none.fl_str_mv | Faustino, Nelson |
| dc.date.Accepted.fl_str_mv | 2023-07-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2023-10-10T10:37:57Z |
| dc.date.embargoed.fl_str_mv | 2023-10-10T10:37:57Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10773/39466 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Wiley |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Fractional semidiscrete Dirac operators Riemann–Liouville fractional derivative Fractional discrete Laplacian |
| dc.title.fl_str_mv | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L\'evy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z}^n\times[0,\infty)$ ($h>0$), resembling to fractional semidiscrete counterparts of the so-called parabolic Dirac operators. The methods adopted here are fairly operational, relying mostly on the algebraic manipulations involving Clifford algebras, discrete Fourier analysis techniques as well as standard properties of the analytic fractional semidiscrete semigroup $\left\{\exp(-te^{i\theta}(-\Delta_h)^{\alpha})\right\}_{t\geq 0}$, carrying the parameter constraints $0<\alpha\leq 1$ and $|\theta|\leq \frac{\alpha \pi}{2}$. The results obtained involve the study of Cauchy problems on $h\mathbb{Z}^n\times[0,\infty)$. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ria_59da3054898a2ce34df875a74dc316e4 |
| identifier.url.fl_str_mv | http://hdl.handle.net/10773/39466 |
| instacron_str | ua |
| institution | Universidade de Aveiro |
| instname_str | Universidade de Aveiro |
| language | eng |
| network_acronym_str | ria |
| network_name_str | RIA - Repositório Institucional da Universidade de Aveiro |
| oai_identifier_str | oai:ria.ua.pt:10773/39466 |
| organization_str_mv | urn:organizationAcronym:ua |
| person_str_mv | Faustino, Nelson |
| publishDate | 2023 |
| publisher.none.fl_str_mv | Wiley |
| reponame_str | RIA - Repositório Institucional da Universidade de Aveiro |
| repository_id_str | urn:repositoryAcronym:ria |
| service_str_mv | urn:repositoryAcronym:ria |
| spelling | pt_PTIn this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L\'evy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z}^n\times[0,\infty)$ ($h>0$), resembling to fractional semidiscrete counterparts of the so-called parabolic Dirac operators. The methods adopted here are fairly operational, relying mostly on the algebraic manipulations involving Clifford algebras, discrete Fourier analysis techniques as well as standard properties of the analytic fractional semidiscrete semigroup $\left\{\exp(-te^{i\theta}(-\Delta_h)^{\alpha})\right\}_{t\geq 0}$, carrying the parameter constraints $0<\alpha\leq 1$ and $|\theta|\leq \frac{\alpha \pi}{2}$. The results obtained involve the study of Cauchy problems on $h\mathbb{Z}^n\times[0,\infty)$.application/pdfengWileypt_PTOn fractional semidiscrete Dirac operators of Lévy-Leblond typeFaustino, NelsonHandlehttp://hdl.handle.net/10773/39466ISSNIsPartOf0025-584XDOIIsPartOf10.1002/mana.2021002342023-10-10T10:37:57Z2023-07-01T00:00:00Z2023-07http://purl.org/coar/access_right/c_abf2open accesspt_PTFractional semidiscrete Dirac operatorspt_PTRiemann–Liouville fractional derivativept_PTFractional discrete Laplacian537983 byteshttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://ria.ua.pt/bitstream/10773/39466/1/Mathematische%20Nachrichten%20-%202023%20-%20Faustino.pdfliteraturehttp://purl.org/coar/resource_type/c_6501journal article |
| spellingShingle | On fractional semidiscrete Dirac operators of Lévy-Leblond type Faustino, Nelson Fractional semidiscrete Dirac operators Riemann–Liouville fractional derivative Fractional discrete Laplacian |
| status | SINGLETON |
| subject.fl_str_mv | Fractional semidiscrete Dirac operators Riemann–Liouville fractional derivative Fractional discrete Laplacian |
| title | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| title_full | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| title_fullStr | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| title_full_unstemmed | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| title_short | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| title_sort | On fractional semidiscrete Dirac operators of Lévy-Leblond type |
| topic | Fractional semidiscrete Dirac operators Riemann–Liouville fractional derivative Fractional discrete Laplacian |
| topic_facet | Fractional semidiscrete Dirac operators Riemann–Liouville fractional derivative Fractional discrete Laplacian |
| url | http://hdl.handle.net/10773/39466 |
| visible | 1 |