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