Designing Local Orthogonal Bases on Finite Groups I: Abelian Case
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چکیده
(a) (b) (c) b b ˆ Figure 1: Geometric interpretation of the orthogonalization procedure using the Fourier transform as a tool. The group is ? = fI; V g, where V performs the exchange of the components of vectors from R 2. (a) Projection of b on the ?-invariant subspaces relative to U 1 and U ?1. (b) Normalization of the two projections. (c) Recombination of the normalized projections yielding the generating vector ^ b. It is now clear that ^ b and V ^ b are orthogonal.
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تاریخ انتشار 1999