Geodesic
A generalization of Calderon's theorem. Discretization of continuous wavelet transforms
Numerical methods and programming, Tome 10 (2009) no. 1, pp. 49-55

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Calderon's theorem is generalized to the set of periodic functions belonging to the space $L^2([0,1)$. The discretization of the direct and inverse wavelet transforms are realized on the basis of the discrete Fourier transform, which allows one to develop efficient computational algorithms. The Mexican hat wavelet is considered as an example. The work is supported by the Russian Foundation for Basic Research (project no. 08-01-00285).
Keywords: wavelets; Fourier transform; convolution operator. 
@article{VMP_2009_10_1_a5,
     author = {Ya. M. Zhileikin},
     title = {A generalization of {Calderon's} theorem. {Discretization} of continuous wavelet transforms},
     journal = {Numerical methods and programming},
     pages = {49--55},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a5/}
}
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Ya. M. Zhileikin. A generalization of Calderon's theorem. Discretization of continuous wavelet transforms. Numerical methods and programming, Tome 10 (2009) no. 1, pp. 49-55. http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a5/