A note on integer translates of a square integrable function on $\mathbb R$
Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 593-597
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Maciej Paluszyński 1
@article{10_4064_cm118_2_15,
author = {Maciej Paluszy\'nski},
title = {A note on integer translates of a square integrable function on $\mathbb R$},
journal = {Colloquium Mathematicum},
pages = {593--597},
year = {2010},
volume = {118},
number = {2},
doi = {10.4064/cm118-2-15},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm118-2-15/}
}
TY - JOUR AU - Maciej Paluszyński TI - A note on integer translates of a square integrable function on $\mathbb R$ JO - Colloquium Mathematicum PY - 2010 SP - 593 EP - 597 VL - 118 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm118-2-15/ DO - 10.4064/cm118-2-15 LA - en ID - 10_4064_cm118_2_15 ER -
Maciej Paluszyński. A note on integer translates of a square integrable function on $\mathbb R$. Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 593-597. doi: 10.4064/cm118-2-15
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