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   -> Volume 6, Issue 4

Preprint: Diagonalization of ...
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Lindberg Martin (

PostPosted: Wed Mar 19, 1997 9:49 pm    
Subject: Preprint: Diagonalization of ...
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#6 Preprint: Diagonalization of ...

Dear Editor,

We submit a preprint on how to diagonalize certain operators
in biorthogonal wavelet bases.

Fredrik and Martin

Diagonalization of Homogeneous Linear Operators in
Biorthogonal Wavelet Bases

We show how it is possible to diagonalize a certain class of
homogeneous linear operators in a biorthogonal wavelet basis. Given
a linear operator and a biorthogonal wavelet basis we construct a
new biorthogonal wavelet basis such that by analyzing a function in
the new basis and multiplying the wavelet coefficients by a scale
dependent factor we get the wavelet coefficients of the transformed
function in the original wavelet basis. Differentiation and integration,
the Riesz potential and the Hilbert transform belong to this class
of operators. Finally we generalize the method to several
dimensions including non-separable bases.

Fredrik Ekstedt and Martin Lindberg

Chalmers University of Technology
S-412 96 Gothenburg


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