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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 11, Issue 10


Volume 13 (2015)

Closure of dilates of shift-invariant subspaces

Moisés Soto-Bajo
  • Department of Mathematics, Faculty of Sciences, Autonomous University of Madrid, Cantoblanco, 28049, Madrid, Spain
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Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0275-z


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.

MSC: 42C15; 42C30; 42C40

Keywords: Multiresolution analysis; Generalized multiresolution analysis; Spectral function; Fourier transform; Approximate continuity

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About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01

Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1785–1799, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0275-z.

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