Publication: Discrete-continuous Jacobi-Sobolev spaces and Fourier series
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.affiliation.grupoinv | UC3M. Grupo de Investigación: Análisis Aplicado | es |
dc.contributor.author | Díaz González, Abel | |
dc.contributor.author | Marcellán Español, Francisco José | |
dc.contributor.author | Pijeira Cabrera, Héctor Esteban | |
dc.contributor.author | Urbina, Wilfredo | |
dc.contributor.funder | Ministerio de Economía y Competitividad (España) | es |
dc.date.accessioned | 2022-01-25T12:22:14Z | |
dc.date.available | 2022-01-25T12:22:14Z | |
dc.date.issued | 2021-03 | |
dc.description.abstract | Let p≥1,ℓ∈N,α,β>−1 and ϖ=(ω0,ω1,…,ωℓ−1)∈Rℓ. Given a suitable function f, we define the discrete–continuous Jacobi–Sobolev norm of f as: ∥f∥s,p:=(∑k=0ℓ−1∣∣f(k)(ωk)∣∣p+∫1−1∣∣f(ℓ)(x)∣∣pdμα,β(x))1p, where dμα,β(x)=(1−x)α(1+x)βdx. Obviously, ∥⋅∥s,2=⟨⋅,⋅⟩s−−−−√, where ⟨⋅,⋅⟩s is the inner product ⟨f,g⟩s:=∑k=0ℓ−1f(k)(ωk)g(k)(ωk)+∫1−1f(ℓ)(x)g(ℓ)(x)dμα,β(x). In this paper, we summarize the main advances on the convergence of the Fourier–Sobolev series, in norms of type Lp, in the continuous and discrete cases, respectively. Additionally, we study the completeness of the Sobolev space of functions associated with the norm ∥⋅∥s,p and the denseness of the polynomials. Furthermore, we obtain the conditions for the convergence in ∥⋅∥s,p norm of the partial sum of the Fourier–Sobolev series of orthogonal polynomials with respect to ⟨⋅,⋅⟩s. | en |
dc.description.sponsorship | Authors thank the valuable comments by the referees. Their suggestions have contributed to improve the presentation of this manuscript. The research of F. Marcellán and H. Pijeira-Cabrera was partially supported by Spanish State Research Agency, under Grant PGC2018-096504-B-C33. The research of A. Díaz-González was supported by the Research Fellowship Program, Ministry of Economy and Competitiveness of Spain, under grant BES-2016-076613. | en |
dc.format.extent | 28 | |
dc.identifier.bibliographicCitation | Díaz-González, A., Marcellán, F., Pijeira-Cabrera, H. & Urbina, W. (2020). Discrete–Continuous Jacobi–Sobolev Spaces and Fourier Series. Bulletin of the Malaysian Mathematical Sciences Society, 44(2), 571–598. | en |
dc.identifier.doi | https://doi.org/10.1007/s40840-020-00950-7 | |
dc.identifier.issn | 0126-6705 | |
dc.identifier.publicationfirstpage | 571 | |
dc.identifier.publicationissue | 2 | |
dc.identifier.publicationlastpage | 598 | |
dc.identifier.publicationtitle | Bulletin of the Malaysian Mathematical Sciences Society | en |
dc.identifier.publicationvolume | 44 | |
dc.identifier.uri | https://hdl.handle.net/10016/33956 | |
dc.identifier.uxxi | AR/0000026672 | |
dc.language.iso | eng | en |
dc.publisher | Springer Nature | en |
dc.relation.projectID | Gobierno de España. BES-2016-076613 | es |
dc.relation.projectID | Gobierno de España. PGC2018-096504-B-C33 | es |
dc.rights | © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2020. | en |
dc.rights.accessRights | open access | en |
dc.subject.eciencia | Matemáticas | es |
dc.subject.other | Sobolev orthogonal polynomials | en |
dc.subject.other | Jacobi polynomials | en |
dc.subject.other | Fourier series | en |
dc.title | Discrete-continuous Jacobi-Sobolev spaces and Fourier series | en |
dc.type | research article | * |
dc.type.hasVersion | AM | * |
dspace.entity.type | Publication |
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