Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor
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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.
Share and Cite
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
Keywords
- Parseval frames multiwavelet
- Fourier multipliers
- matrix Fourier multiwavelet frames multipliers
- frame wavelet set
MSC
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