Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor


Authors

Fengjuan Zhu - School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China. Yongdong Huang - School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China. Shengnan Shi - School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China. Xiao Tan - School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China. Juan Zhao - School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China.


Abstract

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 \(N_1\times N\) matrices with \(L^\infty\) function entries, and maps Parseval multiwavelet frames of length \(N\) to Parseval multiwavelet frames of length \(N_1\). 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.


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ISRP Style

Fengjuan Zhu, Yongdong Huang, Shengnan Shi, Xiao Tan, Juan Zhao, Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4915--4929

AMA Style

Zhu Fengjuan, Huang Yongdong, Shi Shengnan, Tan Xiao, Zhao Juan, Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor. J. Nonlinear Sci. Appl. (2017); 10(9):4915--4929

Chicago/Turabian Style

Zhu, Fengjuan, Huang, Yongdong, Shi, Shengnan, Tan, Xiao, Zhao, Juan. "Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4915--4929


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