Wavelet representations and Fock space on positive matrices
Classical Analysis and ODEs
2007-05-23 v1 Operator Algebras
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.
Cite
@article{arxiv.math/0204034,
title = {Wavelet representations and Fock space on positive matrices},
author = {P. E. T. Jorgensen and D. W. Kribs},
journal= {arXiv preprint arXiv:math/0204034},
year = {2007}
}
Comments
32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Anal