Abstract
Let M be a d × d expansive matrix, and FL 2(Ω) be a reducing subspace of L 2(ℝ d ). This paper characterizes bounded measurable sets in ℝ d which are the supports of Fourier transforms of M-refinable frame functions. As applications, we derive the characterization of bounded measurable sets as the supports of Fourier transforms of FMRA (W-type FMRA) frame scaling functions and MRA (W-type MRA) scaling functions for FL 2(Ω), respectively. Some examples are also provided.
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