Closure of dilates of shift-invariant subspaces

Moisés Soto-Bajo

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1785-1799
  • ISSN: 2391-5455

Abstract

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Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a point of A*-approximate continuity of the Fourier transform of any semiorthogonal tight frame wavelet if we assume this value to be zero.

How to cite

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Moisés Soto-Bajo. "Closure of dilates of shift-invariant subspaces." Open Mathematics 11.10 (2013): 1785-1799. <http://eudml.org/doc/269595>.

@article{MoisésSoto2013,
abstract = {Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a point of A*-approximate continuity of the Fourier transform of any semiorthogonal tight frame wavelet if we assume this value to be zero.},
author = {Moisés Soto-Bajo},
journal = {Open Mathematics},
keywords = {Multiresolution analysis; Generalized multiresolution analysis; Spectral function; Fourier transform; Approximate continuity; multiresolution analysis; generalized multiresolution analysis; spectral function; approximate continuity},
language = {eng},
number = {10},
pages = {1785-1799},
title = {Closure of dilates of shift-invariant subspaces},
url = {http://eudml.org/doc/269595},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Moisés Soto-Bajo
TI - Closure of dilates of shift-invariant subspaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1785
EP - 1799
AB - Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a point of A*-approximate continuity of the Fourier transform of any semiorthogonal tight frame wavelet if we assume this value to be zero.
LA - eng
KW - Multiresolution analysis; Generalized multiresolution analysis; Spectral function; Fourier transform; Approximate continuity; multiresolution analysis; generalized multiresolution analysis; spectral function; approximate continuity
UR - http://eudml.org/doc/269595
ER -

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