Refinability, reversed

August 10th, 2005 ~ Posted in: General

Recall that a function f is refinable iff there is a sequence of coefficients \alpha_k such that f(x) = \sum_{k=1}^\infty \alpha_k f(x-k) for all x. So presumably, if I give you a refinable function, you can find the coefficients of refinability.

Question: if I give you a sequence \alpha_k (in l^2(\N) for simplicity), can you find an f \in L^2(\R) that has that sequence as its coefficients of refinability?

General ~

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