This dissertation develops a new general method of solving Prony's
problem. Two special cases of this new method have been developed
previously. They are the Matrix Pencil and the Osculatory
Interpolation. The dissertation shows that they are instances of a
more general solution type which allows a wide ranging class of
linear functional to be used in the solution of the problem. This
class provides a continuum of functionals which provide new methods
that can be used to solve Prony's problem.
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