ON LOW PASS FILTERS IN A FRAME MULTIRESOLUTION ANALYSIS

抄録

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.