A generalization of Calderon’s theorem. Discretization of continuous wavelet transforms


  • Ya.M. Zhileikin Lomonosov Moscow State University


wavelets, Fourier transform, convolution operator


Calderon’s theorem is generalized to the set of periodic functions belonging to the space L2(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).

Author Biography

Ya.M. Zhileikin


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  2. Чуи К. Введение в вэйвлеты. М.: Мир, 2001.
  3. Фрейзер М. Введение в вэйвлеты в свете линейной алгебры. М.: БИНОМ, 2007.
  4. Жилейкин Я.М., Осипик Ю.И. О погрешности и алгоритмах численной реализации непрерывных вэйвлет-преобразований // Журн. вычисл. матем. и матем. физики. 2005. 45, № 12. 2091-2101.



How to Cite

Жилейкин Я.М. A Generalization of Calderon’s Theorem. Discretization of Continuous Wavelet Transforms // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2008. 10. 49-55



Section 1. Numerical methods and applications

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