Abstract
Based on interpolatory Hermite splines on rectangular domains, the interpolatory curl-free wavelets and its duals are first constructed. Then we use it to characterize a class of vector-valued Besov spaces. Finally, the stability of wavelets that we constructed are studied.MR(2000) Subject Classification: 42C15; 42C40.
Highlights
1 Introduction Due to its potential use in many physical problems, like the simulation of incompressible fluids or in electromagnetism, curl-free wavelet bases have been advocated in several articles and most of the study focus on the cases of R2 and R3 [1,2,3,4]
The stability and the characterization of function spaces are necessary in some applications, such as the adaptive wavelet methods
We mainly study the interpolatory 3D curl-free wavelet bases on the cube and its applications for characterizing the vector-valued Besov spaces
Summary
Due to its potential use in many physical problems, like the simulation of incompressible fluids or in electromagnetism, curl-free wavelet bases have been advocated in several articles and most of the study focus on the cases of R2 and R3 [1,2,3,4]. We mainly study the interpolatory 3D curl-free wavelet bases on the cube and its applications for characterizing the vector-valued Besov spaces. We study the stability of the corresponding curl-free wavelets. Let I ⊆ {1, 2, 3} =: I0, define scaling functions φmI (x1, x2, x3) =: ξmI v,v(xv), m = (m1, m2, m3)T ∈ {1, 2}3 v=1 with ξμI ,v =
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