Closure of dilates of shift-invariant subspaces
Keyword(s):
AbstractLet 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.
1997 ◽
Vol 125
(11)
◽
pp. 3275-3278
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2014 ◽
Vol 18
(2)
◽
pp. 57-90
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Keyword(s):