  This paper presents some properties and applications of "transversal
operators". Two transversal operators are presented: a "translation" operator T
and a "dilation" operator D. Such operators are used in common analysis systems
including Fourier series analysis, Fourier analysis, Gabor analysis,
multiresolution analysis (MRA), and wavelet analysis. Like the unitary Fourier
transform operator F, the transversal operators T and D are unitary.
Demonstrations of the usefulness of these three unitary operators are found in
the proofs of results found in some common analytic systems including MRA
analysis and wavelet analysis.
