Structure of the Set of Dyadic Pfw’s
نویسنده
چکیده
The purpose of this paper is to reveal the deep and rich structure of the set of Parseval frame wavelets. Two main directions are pursued. First, we study the reproducing properties of the translates of a Parseval frame wavelet within the closed linear span that the translates generate. In particular, we show that the translates need not have good reproducing properties, even though the translates and dilates form a Parseval frame. Second, we describe the effect of a semiorthogonalization procedure on the set of Parseval frame wavelets. Several examples illustrating the various possibilities are given.
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