Wavelet representations and Fock space on positive matrices

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We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.
32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Anal

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Classical Analysis and ODEs, Operator Algebras, [2000] 42C40, 42A16, 43A65, 42A65

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http://salesiana.dossiersoluciones.com/handle/123456789/63702

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204034
 http://arxiv.org/abs/math/0204034
 J. Funct. Anal. 197 (2003), 526-559
 doi:10.1016/S0022-1236(02)00026-5

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arXiv