Irregular Wavelet Frames and Gabor Frames |
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Authors: | Ole Christensen Sergio Favier Felipe Zó |
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Affiliation: | 1.Department of Mathematics,Technical University of Denmark,Lyngby,Denmark;2.Instituto de Matemática Aplicada San Luis,Universidad Nacional de San Luis Consejo Nacional de Investigaciones Científicasy Técnicas,San Luis,Argentina |
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Abstract: | Given g∈L2(R n ), we consider irregular wavelet for the form\(\left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\lambda _j \) > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L2(R n ) are given. For a class of functions g∈L22(R n ) we prove that certain growth conditions on {λ j } will frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system\(\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} \)to be a frame. |
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