Journal article

Authors list: Buhmann, Martin; Jaeger, Janin; Xu, Yuan

Publication year: 2024

Journal: Mathematische Zeitschrift

Volume number: 306

Issue number: 3

ISSN: 0025-5874

eISSN: 1432-1823

Open access status: Hybrid

DOI Link: https://doi.org/10.1007/s00209-024-03440-9

Publisher: Springer

Abstract: 
We study the l(1)-summability of functions in the d-dimensional torus T-d and so-called l(1)-invariant functions. Those are functions on the torus whose Fourier coefficients depend only on the l(1)-norm of their indices. Such functions are characterized as divided differences that have cos theta(1),...,cos theta(d)as knots for(theta(1)...,theta(d))is an element of T-d. It leads us to consider the d-dimensional 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

Harvard Citation style: Buhmann, M., Jaeger, J. and Xu, Y. (2024) l¹-summability and Fourier series of B-splines with respect totheir knots, Mathematische Zeitschrift, 306(3), Article 53. https://doi.org/10.1007/s00209-024-03440-9

APA Citation style: Buhmann, M., Jaeger, J., & Xu, Y. (2024). l¹-summability and Fourier series of B-splines with respect totheir knots. Mathematische Zeitschrift. 306(3), Article 53. https://doi.org/10.1007/s00209-024-03440-9