Representation and inequalities involving continuous linear functionals and fractional derivatives

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dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
dc.contributor.authorJornet, Marc
dc.contributor.authorNieto Roig, Juan José
dc.date.accessioned2026-03-24T12:48:09Z
dc.date.available2026-03-24T12:48:09Z
dc.date.issued2024-10-29
dc.date.updated2025-12-04T09:34:42Z
dc.description.abstractWe investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).en
dc.description.peerreviewedSI
dc.description.sponsorshipThe research of the author Juan J. Nieto was supported by the Agencia Estatal de Investigación (AEI) of Spain Grant PID2020-113275GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, by the “European Union” and Xunta de Galicia, grant ED431C 2023/12 for Competitive Reference Research Groups (2023–2026).
dc.identifier.citationJornet, M., & Nieto, J. J. (2025). Representation and inequalities involving continuous linear functionals and fractional derivatives. Advances in Operator Theory, 10(1). https://doi.org/10.1007/S43036-024-00397-8
dc.identifier.doi10.1007/S43036-024-00397-8
dc.identifier.eissn2538-225X
dc.identifier.essn2538-225X
dc.identifier.urihttps://hdl.handle.net/10347/46490
dc.issue.number1
dc.journal.titleAdvances in Operator Theory
dc.language.isoeng
dc.publisherSpringer
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113275GB-I00/ECUACIONES DIFERENCIALES ORDINARIAS NO LINEALES Y APLICACIONES
dc.relation.publisherversionhttps://doi.org/10.1007/s43036-024-00397-8
dc.rights© The Author(s) 2024
dc.rightsAttribution 4.0 Internationalen
dc.rights.accessRightsopen access
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.sourceAdvances in Operator Theory
dc.subjectRepresentation of functionals
dc.subjectInequalities
dc.subjectDifferintegral operators
dc.subjectRiemann-Liouville fractional calculus
dc.titleRepresentation and inequalities involving continuous linear functionals and fractional derivativesen
dc.typejournal article
dc.type.hasVersionVoR
dc.volume.number10
dspace.entity.typePublication
oaire.awardNumberMCIN/AEI/10.13039/501100011033
oaire.awardNumber2023–2026
oaire.funderIdentifier10.13039/501100000780
oaire.funderIdentifier10.13039/501100008530
oaire.funderIdentifier10.13039/501100011033
oaire.funderIdentifier10.13039/501100010801
oaire.funderNameEuropean Commission
oaire.funderNameEuropean Regional Development Fund
oaire.funderNameAgencia Estatal de Investigación
oaire.funderNameXunta de Galicia
relation.isAuthorOfPublication85e127ae-7ec7-48e4-bb4a-8eb83882ea26
relation.isAuthorOfPublication.latestForDiscovery85e127ae-7ec7-48e4-bb4a-8eb83882ea26

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