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2013 | 11 | 10 | 1785-1799

Tytuł artykułu

Closure of dilates of shift-invariant subspaces

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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.










Opis fizyczny




  • Department of Mathematics, Faculty of Sciences, Autonomous University of Madrid, Cantoblanco, 28049, Madrid, Spain


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