OPERATOR-ADAPTED WAVELETS: CONNECTION WITH THE STRANG–FIX CONDITIONS

Author:

ZAKHAROV VICTOR G.1

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. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

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

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