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Closure of dilates of shift-invariant subspaces

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Soto-Bajo M.

Open Mathematics

2013

tom 11

nr 10

1785-1799

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.

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1 Open Mathematics

1 Soto-Bajo M.

1 2013

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Closure of dilates of shift-invariant subspaces