Variations around a general quantum operator

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dc.contributor.authorCardoso, José Luís dos Santospt_PT
dc.date.accessioned2022-07-25T15:23:53Z
dc.date.available2022-07-25T15:23:53Z
dc.date.issued2020-02-17
dc.description.abstractLet I ⊆ R be an interval and β : I → I a strictly increasing and continuous function with a unique fixed point s0 ∈ I that satisfies (s0 − t)(β(t) − t) ≥ 0 for all t ∈ I, where the equality holds only when t = s0. For appropriate choices of the function β, the quantum operator defined by Hamza et al., Dβ[ f ](t) := f β(t) − f (t) β(t) − t if t = s0 and Dβ[ f ](s0) := f (s0) if t = s0, generalizes both the Jackson q-operator Dq and the Hahn (quantum derivative) operator, Dq,ω. With respect to the inverse of this general quantum difference operator, the β-integral, we study properties of the corresponding Lebesgue spaces L p β ([a, b]).pt_PT
dc.identifier.citationCardoso, J.L. Variations around a general quantum operator. Ramanujan J 54, 555–569 (2021). https://doi.org/10.1007/s11139-019-00210-8pt_PT
dc.identifier.urihttps://doi.org/10.1007/s11139-019-00210-8
dc.identifier.urihttp://hdl.handle.net/10348/11332
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringerpt_PT
dc.relation.ispartofCM - Centro de Matemáticapt_PT
dc.rightsrestricted accesspt_PT
dc.subjectGeneral quantum difference operatorpt_PT
dc.subjectβ-derivativept_PT
dc.subjectβ-integralpt_PT
dc.subjectβ-Lebesgue spacespt_PT
dc.subjectq-Analoguespt_PT
dc.subjectJackson q-Integralpt_PT
dc.titleVariations around a general quantum operatorpt_PT
dc.typejournal articlept_PT
degois.publication.firstPage555pt_PT
degois.publication.issue54pt_PT
degois.publication.lastPage569pt_PT
degois.publication.volume2021pt_PT
dspace.entity.typePublicationen
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