Wavelet representations and Fock space on positive matrices |
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Authors: | PET Jorgensen DW Kribs |
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Institution: | Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA |
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Abstract: | 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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Keywords: | 42C40 42A16 43A65 42A65 |
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