l1-summability and Fourier series of B-splines with respect to their knots

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dc.contributor.authorBuhmann, Martin
dc.contributor.authorJäger, Janin
dc.contributor.authorXu, Yuan
dc.date.accessioned2024-11-28T07:02:53Z
dc.date.available2024-11-28T07:02:53Z
dc.date.issued2024
dc.description.abstractWe study the l1-summability of functions in the d-dimensional torus Td and so-called l1-invariant functions. Those are functions on the torus whose Fourier coefficients depend only on the l1-norm of their indices. Such functions are characterized as divided differences that have cos θ1, . . . , cos θd as knots for (θ1 . . . , θd ) ∈ Td . It leads us to consider the ddimensional Fourier series of univariate B-splines with respect to its knots, which turns out to enjoy a simple bi-orthogonality that can be used to obtain an orthogonal series of the B-spline function.
dc.description.sponsorshipDeutsche Forschungsgemeinschaft (DFG); ROR-ID:018mejw64
dc.identifier.urihttps://jlupub.ub.uni-giessen.de/handle/jlupub/19951
dc.identifier.urihttps://doi.org/10.22029/jlupub-19306
dc.language.isoen
dc.rightsNamensnennung 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddcddc:510
dc.subject.ddcddc:004
dc.titlel1-summability and Fourier series of B-splines with respect to their knots
dc.typearticle
local.affiliationFB 07 - Mathematik und Informatik, Physik, Geographie
local.projectProjektnummer: 461449252
local.source.articlenumber53
local.source.epage16
local.source.journaltitleMathematische Zeitschrift
local.source.spage1
local.source.urihttps://doi.org/10.1007/s00209-024-03440-9
local.source.volume306

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