Closure of dilates of shift-invariant subspaces

• Autorzy: Moisés Soto-Bajo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 42C30: Completeness of sets of functions
• 42C15: General harmonic expansions, frames

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1785-1799

Daty

wydano

2013-10-01

online

2013-07-20

Twórcy

autor

Moisés Soto-Bajo

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

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Identyfikatory

DOI

10.2478/s11533-013-0275-z