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| Parseval Frame Wavelet Multipliers in L2（Rd） | |
| 引用本文： | Zhongyan LI,Xianliang SHI. Parseval Frame Wavelet Multipliers in L2（Rd）[J]. 数学年刊B辑(英文版), 2012, 33(6): 949-960. DOI: 10.1007/s11401-012-0739-7 |
| 作者姓名： | Zhongyan LI Xianliang SHI |
| 作者单位： | [1]College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing （HPCSIP）, Ministry of Education of China, Hunan Normal University, Changsha 410081, China; Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China. [2]College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing （HPCSIP）, Ministry of Education of China, Hunan Normal University, Changsha 410081, China. |
| 基金项目： | Project Supported by the National Natural Science Foundation of China （Nos. 11071065, 11101142, 11171306, 10671062）, the China Postdoctoral Science Foundation （No. 20100480942）, the Doctoral Program Foundation of the Ministry of Education of China （No. 20094306110004） and the Program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province. |
| 摘 要： | |
| 关 键 词： | 框架 小波 乘数 傅立叶逆变换 可测函数 傅立叶变换 DET 矩阵A |
Parseval Frame Wavelet Multipliers in $L^2(mathbb{R}^d)$ |
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| Zhongyan LI and Xianliang SHI. Parseval Frame Wavelet Multipliers in $L^2(mathbb{R}^d)$[J]. Chinese Annals of Mathematics,Series B, 2012, 33(6): 949-960. DOI: 10.1007/s11401-012-0739-7 | |
| Authors: | Zhongyan LI and Xianliang SHI |
| Affiliation: | 1. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP), Ministry of Education of China, Hunan Normal University, Changsha, 410081, China 2. Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China |
| Abstract: | Let A be a d × d real expansive matrix. An A-dilation Parseval frame wavelet is a function ?? ?? L 2(? d ), such that the set $ left{ {left| {det A} right|^{frac{n} {2}} psi left( {A^n t - ell } right):n in mathbb{Z},ell in mathbb{Z}^d } right} $ forms a Parseval frame for L 2(? d ). A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of d??? is an A-dilation Parseval frame wavelet whenever ?? is an A-dilation Parseval frame wavelet, where ??? denotes the Fourier transform of ??. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with |det(A)| = 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L 2(? d ) is discussed. |
| Keywords: | Parseval frame wavelet Wavelet multiplier Frame multiresolutionanalysis |
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