Tohoku Mathematical Journal
2011
September
SECOND SERIES VOL. 63, NO. 3

Tohoku Math. J.
63 (2011), 427-439

Title ON LOW PASS FILTERS IN A FRAME MULTIRESOLUTION ANALYSIS

Author Angel San Antolín

(Received July 16, 2010)
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.

2000 Mathematics Subject Classification. Primary 42C15; Secondary 47A75, 42B99.
Key words and phrases. Approximate continuity, Fourier transform, frame multiresolution analysis, low pass filter, scaling function.

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