|
|
| |
| Parseval Frame Wavelet Multipliers in $L^2(\mathbb{R}^d)$ |
| |
Citation： |
Zhongyan LI,Xianliang SHI.Parseval Frame Wavelet Multipliers in $L^2(\mathbb{R}^d)$[J].Chinese Annals of Mathematics B,2012,33(6):949~960 |
| Page view： 1863
Net amount： 1788 |
Authors： |
Zhongyan LI; Xianliang SHI; |
Foundation： |
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. |
|
|
| Abstract： |
Let $A$ be a $d\times d$ real expansive matrix. An $A$-dilation Parseval frame wavelet is a function $\psi\in L^{2}(\R^{d})$, such that the set $\{|\det A|^{\frac{n}{2}}\psi(A^{n}\t - \ell): n\in\Z, \ell\in\Z^{d}\}$ forms a Parseval frame for $L^{2}(\R^{d})$. A measurable function $f$ is called an $A$-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of $f\wh{\psi}$ is an $A$-dilation Parseval frame wavelet whenever $\psi$ is an $A$-dilation Parseval frame wavelet, where $\wh{\psi}$ denotes the Fourier transform of $\psi$. 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 $L^{2}(\R^{d})$ is discussed. |
Keywords： |
Parseval frame wavelet, Wavelet multiplier, Frame multiresolution analysis |
Classification： |
42C15, 42C40 |
|
|
Download PDF Full-Text
|
|
|
|
