Abstract
We give necessary and sufficient conditions for a measurable function to be a low pass filter associated to a scaling function in a frame multiresolution analysis. Those conditions involve the class of real-valued bounded measurable functions such that the origin is a point of approximate continuity of such functions. The main result here is proved in a general context where the considered dilation is given by a fixed expansive linear map.
Citation
Angel San Antolín. "On low pass filters in a frame multiresolution analysis." Tohoku Math. J. (2) 63 (3) 427 - 439, 2011. https://doi.org/10.2748/tmj/1318338950
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