Affiliation:
1. Institute of Continuum Mechanics of Russian Academy of Sciences, Perm 614013, Russia
Abstract
In this paper, we present an explicit method to construct directly in the x-domain compactly supported scaling functions corresponding to the wavelets adapted to a sum of differential operators with constant coefficients. Here the adaptation to an operator is taken to mean that the wavelets give a diagonal form of the operator matrix. We show that the biorthogonal compactly supported wavelets adapted to a sum of differential operators with constant coefficients are closely connected with the representation of the null-space of the adjoint operator by the corresponding scaling functions. We consider the necessary and sufficient conditions (actually the Strang–Fix conditions) on integer shifts of a compactly supported function (distribution) f ∈ S'(ℝ) to represent exactly any function from the null-space of a sum of differential operators with constant coefficients.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Information Systems,Signal Processing
Cited by
4 articles.
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1. Smooth reverse subdivision of uniform algebraic hyperbolic B-splines and wavelets;International Journal of Wavelets, Multiresolution and Information Processing;2021-05-17
2. Reproducing fractional monomials: Weakening of the Strang–Fix conditions;International Journal of Wavelets, Multiresolution and Information Processing;2020-11-12
3. Reproducing solutions to PDEs by scaling functions;International Journal of Wavelets, Multiresolution and Information Processing;2020-02-07
4. ELLIPTIC SCALING FUNCTIONS AS COMPACTLY SUPPORTED MULTIVARIATE ANALOGS OF THE B-SPLINES;International Journal of Wavelets, Multiresolution and Information Processing;2014-03