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Volume 20,     Number 3,     Fall 2012

 

REPRESENTATION OF DIFFERENTIAL
OPERATORS IN 2D NONSEPARABLE
WAVELET BASES
MOHAMED ALI HAJJI AND RÉMI VAILLANCOURT

Abstract. In this paper, we consider the nonstandard representation of general partiial differential operators g(∂x, ∂y) in two-dimensional nonseparable wavelet bases. The function gis assumed to be analytic. The construction of the matrix representation of g(∂x, ∂y) is based on the construction of the matrix representation of the operators ∂x and ∂y, and the analyticity of g. The use of periodized wavelets makes possible the derivation of a closed form formula for the matrix representation of g(∂x, ∂y) in terms of the matrices of ∂x and ∂y.

 

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