We develop an operator-theoretic approach to discrete frame theory on a sep-
arable Hilbert space. We then apply this to an investigation of the structural
properties of systems of unitary operators on Hilbert space which are related to
orthonormal wavelet theory. We also obtain applications of frame theory to group
representations, and of the theory of abstract unitary systems to frames generated
by Gabor type systems.
Key Words and Phrases. Frame, wavelet, complementary frame, frame vec-
tor, super frame, super wavelet, frame representation, Gabor-type unitary system,
Gabor frame, Weyl-Heisenberg frame.