Properties and applications of transversal operators
  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. 
Daniel J. Greenhoe
math.GM