A note on integer translates of a square integrable function on $\mathbb R$

Maciej Paluszyński¹

¹ Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland

Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 593-597.

Résumé

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.

Détail

DOI : 10.4064/cm118-2-15

Keywords: consider subspace mathbb spanned integer shifts function nbsp psi formulate condition family psi cdot n infty infty which equivalent weight function sum infty infty hat psi cdot being nbsp