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Analog radar signal design and digital signal processing -a Heisenberg nilpotent Lie group approach.- Fourier optics from the perspective of the Heisenberg group.- Lie series, Lie transformations, and their applications.- Foundations of a Lie algebraic theory of geometrical optics.- Canonical transforms for paraxial wave optics.- Wave theory of imaging systems.- Invariants and coherent states in fiber optics.- The influence of spherical aberration on gaussian beam propagation.