A note on integer translates of a square integrable function on $\mathbb R$
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 593-597
MSC: Primary 42C40; Secondary 42A20.
DOI: 10.4064/cm118-2-15
Abstract
We consider the subspace of $L^2({\mathbb R})$ spanned by the integer shifts of one function $\psi$, and formulate a condition on the family $\{\psi(\cdot-n)\}_{n=-\infty}^\infty$, which is equivalent to the weight function $\sum_{n=-\infty}^\infty|\hat{\psi}(\cdot+n)|^{2}$ being $>0$ a.e.
