Consider the dilation equation (9.138) with c 0 = 0, c 1 = c 2 = 1,

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Consider the dilation equation (9.138) with c0 = 0, c1 = c2 = 1, so φ(x) = φ(2x − 1) + φ (2x − 2). Prove that ψ(x) = φ(x + 1) satisfies the Haar dilation equation (9.139). Generalize this result to prove that we can always, without loss of generality, assume that c≠ 0 in the general dilation equation (9.138).


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Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

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