I will discuss some recent discoveries that show that a multiresolution structure on a Hilbert space is totally constructible from an integer-valued function m that satisfies a certain consistency inequality.

The background needed to follow this talk is not much more than a comfort level with complex inner products, although I will toward the end have to say words like "Hilbert space," "unitary operator," and "partial isometry" in order to describe what a multiresolution structure is.

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