A fundamental set in $L^2(0,1)$
Volume 199 / 2021
Acta Arithmetica 199 (2021), 269-274
MSC: Primary 11Mxx.
DOI: 10.4064/aa200216-31-8
Published online: 24 March 2021
Abstract
Nyman and Beurling showed that the Riemann hypothesis is equivalent to the density of a certain function space in $L^2(0,1)$, called the Nyman–Beurling space. In this paper, we consider subspaces spanned by generators of the Nyman–Beurling space and give a necessary condition for the generators to be a fundamental set in $L^2(0,1)$.
