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 twodimensional 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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