This paper investigates the structure of general affine subspaces of L2(Rd) . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is ...This paper investigates the structure of general affine subspaces of L2(Rd) . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated by dilating some shift invariant space in this affine subspace, and every non-zero and non-reducing affine subspace is the orthogonal direct sum of a reducing subspace and a purely non-reducing subspace, and every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces when |detA| = 2.展开更多
In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satis...In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet p such that {2J/2b（Mj -k）：j E Z, k c gg} forms a Riesz basis for L2（Ra）. The （anti-）symmetry of such ~b is studied, and some examples are also provided.展开更多
文摘This paper investigates the structure of general affine subspaces of L2(Rd) . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated by dilating some shift invariant space in this affine subspace, and every non-zero and non-reducing affine subspace is the orthogonal direct sum of a reducing subspace and a purely non-reducing subspace, and every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces when |detA| = 2.
文摘In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet p such that {2J/2b（Mj -k）：j E Z, k c gg} forms a Riesz basis for L2（Ra）. The （anti-）symmetry of such ~b is studied, and some examples are also provided.
