Reflection Coefficient (Schur Parameter) Representation for Convex Compact Sets in the Plane

We combine certain results from two disparate areas, kinematics/differential geometry and geophysics/time-series analysis, to obtain a convenient representation for convex compact planar sets in terms of a sequence of complex valued reflection coefficients. This gives a one-to-one relation between any convex compact planar set S and any set of parameters comprising: (a) the coordinates of a reference point in S, (b) the circumference of the set, and (c) a complex reflection coefficient sequence, {k sub 1, k sub 2,...}, such that 1) k sub 1 = 0, 2) |k sub n| N. For a finite duration reflection coefficient sequence such that k sub n = 0, inverted A n > N, if 0