Glasnik Matematicki, Vol. 49, No. 2 (2014), 377-394.

ON TRANSLATION INVARIANT MULTIRESOLUTION ANALYSIS

Angel San Antolín

Departamento de Análisis Matemático, Universidad de Alicante, 03080 Alicante, Spain
e-mail: angel.sanantolin@ua.es


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  n preserving the integer lattice  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.

2010 Mathematics Subject Classification.   42C40, 42C30, 51M15.

Key words and phrases.   Fourier transform, locally nonzero function, low pass filter, scaling function, translation invariant multiresolution analysis.


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DOI: 10.3336/gm.49.2.11


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