Closure of dilates of shift-invariant subspaces

Moisés Soto-Bajo

Open Mathematics, Tome 11 (2013), p. 1785-1799 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2013-01-01

Zbl 1315.42021

EUDML-ID : urn:eudml:doc:269595

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