Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor

This paper investigates matrix Fourier multiwavelet frames multipliers with dilation factor a. First, the definition of matrix Fourier multiwavelet frame multiplier was proposed, which is N1 × N matrices with L∞ function entries, and maps Parseval multiwavelet frames of length N to Parseval multiwavelet frames of length N1. Then, two sufficient conditions of matrix Fourier multiwavelet frame multiplier were given, and two necessary conditions of matrix Fourier multiwavelet frame multiplier were characterized by means of frame wavelet sets. Finally, several numerical examples were constructed. As Fourier wavelet frames multiplier, matrix Fourier multipliers can be used to derive new Parseval multiwavelet frames and can help us better understand the basic of frame theory.