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|Title:||Multiresolution on compact groups||Authors:||Lim, A.
|Issue Date:||15-May-1999||Citation:||Lim, A., Zhu, C.-B. (1999-05-15). Multiresolution on compact groups. Linear Algebra and Its Applications 293 (1-3) : 15-38. ScholarBank@NUS Repository.||Abstract:||Given a compact group M, we define the notion of multiresolution of L2 (M) with respect to an infinite sequence of subgroups G0 ⊆ G1 ⊆ G2 ⊆ ⋯ such that G = ∪∞ k=0 is a dense subgroup of M. We give characterizations of various axioms of multiresolution, demonstrate the existence and give the construction of a wavelet basis for L2 (M). We also construct stationary multiresolution and wavelets from cyclic vectors. An example of multiresolution on a non-abelian compact group is given for the infinite dihedral group, or isomorphically the real orthogonal group in dimension two. © 1999 Published by Elsevier Science Inc. All rights reserved.||Source Title:||Linear Algebra and Its Applications||URI:||http://scholarbank.nus.edu.sg/handle/10635/131453||ISSN:||00243795|
|Appears in Collections:||Staff Publications|
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