Closed subspaces which are attractors for representations of the Cuntz algebras

2002/12/31 by Palle E. T. Jorgensen
Mathematics · #math.OA #math.FA #msc:46L60 #msc:47L30 #msc:42A16 #msc:43A65 #msc:33C45 #msc:42C10 #msc:94A12 #msc:46L45 #msc:42A65 #msc:41A15

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published as Current Trends in Operator Theory and Its Applications (Blacksburg, VA, 2002) (J.A. Ball, J.W. Helton, M. Klaus, and L. Rodman, eds.), Oper. Theory Adv. Appl., vol. 149, Birkhäuser, Basel, 2004, pp. 223-253 · 32 pages, LaTeX2e "birkart" document class; accepted for publication in the Proceedings of the 2002 IWOTA conference at Virginia Tech in Blacksburg, VA. v4 revision: changes and corrections to Theorem 4.4 and Corollary 7.1. Also Theorem 4.4 is relabeled "Proposition 4.4", and clarifying remarks are added

Abstract

We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in L²(R) corresponding to scale number N.

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