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

Volume 118 / 2010

Maciej Paluszyński Colloquium Mathematicum 118 (2010), 593-597 MSC: Primary 42C40; Secondary 42A20. DOI: 10.4064/cm118-2-15


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.


  • Maciej PaluszyńskiInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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