Wavelet representations and Fock space on positive matrices

Details Wavelet representations and Fock space on positive matrices Wavelet representations and Fock space on positive matrices

2002-04-02

arxiv.org/abs/math/0204034v1

J. Funct. Anal. 197 (2003), 526-559

Mathematics

Classical Analysis and ODEs

32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Anal

Scientific paper

10.1016/S0022-1236(02)00026-5

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.

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