Glasnik matematički, Vol. 49 No. 2, 2014.
Original scientific paper
https://doi.org/10.3336/gm.49.2.11
On translation invariant multiresolution analysis
Angel San Antolín
; Departamento de Análisis Matemático, Universidad de Alicante, 03080 Alicante, Spain
Abstract
We give a characterization of the scaling functions and low pass filters in a translation invariant multiresolution analysis on L2(ℝ n). Our conditions involve the notion of locally non-zero function. We write our results in a general context where one considers a dilation given by a fixed expansive linear map on ℝ n preserving the integer lattice ℤ n. Indeed, for any such a linear map we construct a scaling function where the support of the Fourier transform is bounded and does not contain any open neighborhood of the origin.
Keywords
Fourier transform; locally nonzero function; low pass filter; scaling function; translation invariant multiresolution analysis
Hrčak ID:
130891
URI
Publication date:
18.12.2014.
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