We show that a characterization of scaling functions for multiresolution analyses given by Hern\'{a}ndez and Weiss and that a characterization of low-pass filters given by Gundy both hold for multivariable multiresolution analyses.

Keywords:

multivariable multiresolution analysis, low-pass filter, scaling function multivariable multiresolution analysis, low-pass filter, scaling function

MSC Classifications:

42C40, 60G35 show english descriptions Wavelets and other special systems
Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 42C40 - Wavelets and other special systems
60G35 - Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

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