Frames, Riesz systems and multiresolution analysis in Hilbert spaces

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Abstract

The concept of multiresolution analysis (MRA) is introduced for arbitrary separable Hilbert spaces H. It is put in the general terms of unitary operators U1 and U2.1, …, U2.d, d e Z and a generating element f. Each MRA yields a system ¿ = 1kU2,1l1 … U2,dld¿n ¦ N = 0,…, N - 1, k e Z, l e Zd, where the ¿n are related to f. Necessary and sufficient conditions on U1, U2,1,…, U2,d, f and ¿n are given, by means of properties of matrix-valued functions on the unit circle, such that V is a Riesz system or Riesz basis in H.
Original languageEnglish
Pages (from-to)369-382
JournalIndagationes Mathematicae. New Series
Volume10
Issue number3
DOIs
Publication statusPublished - 1999

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