A note on integer translates of a square integrable function on ℝ

@article{MaciejPaluszyński2010,
abstract = {We consider the subspace of L²(ℝ) spanned by the integer shifts of one function ψ, and formulate a condition on the family $\{ψ(·-n)\}_\{n=-∞\}^\{∞\}$, which is equivalent to the weight function $∑_\{n=-∞\}^\{∞\} |ψ̂(·+n)|²$ being > 0 a.e.},
author = {Maciej Paluszyński},
journal = {Colloquium Mathematicae},
keywords = {wavelets; shift-invariant space; integer translates},
language = {eng},
number = {2},
pages = {593-597},
title = {A note on integer translates of a square integrable function on ℝ},
url = {http://eudml.org/doc/286373},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Maciej Paluszyński
TI - A note on integer translates of a square integrable function on ℝ
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 593
EP - 597
AB - We consider the subspace of L²(ℝ) spanned by the integer shifts of one function ψ, and formulate a condition on the family ${ψ(·-n)}_{n=-∞}^{∞}$, which is equivalent to the weight function $∑_{n=-∞}^{∞} |ψ̂(·+n)|²$ being > 0 a.e.
LA - eng
KW - wavelets; shift-invariant space; integer translates
UR - http://eudml.org/doc/286373
ER -