Anisotropic curl-free wavelet bases on the unit cube
Curl-free wavelet bases have been investigated on two-dimensional and three-dimensional space. It is important to construct curl-free wavelet bases on bounded domains. Anisotropic divergence-free wavelets on the hypercube have been studied. This paper is to study anisotropic curl-free wavelets on the unit cube. The authors construct anisotropic curl-free wavelets on the unit cube satisfying specific boundary conditions. These wavelets are stable in curl-free space and the wavelet transform has a fast algorithm. The complement space for curl-free space and a Helmholtz decomposition are given for square integrable space on the unit cube. Besides, the expression of curl and div operators in terms of wavelet coordinates, as well as the corresponding norm equivalences, are also studied and provided. This study on anisotropic curl-free wavelets on bounded domains is systematic and in a constructive way.
scientific article; zbMATH DE number 6149097