l1-summability and Fourier series of B-splines with respect to their knots
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DOI:
https://doi.org/10.22029/jlupub-19306Abstract
We 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.Link to publications or other datasets
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Original publication in
Mathematische Zeitschrift 306 (2024), 1 - 16, 53