Positive Definite Extensions, Canonical Equations and Inverse Problems
Harry Dym, Andrei Iacob · Birkhäuser Basel eBooks · 1984
The intimate connections between a form of the covariance extension problem and the spectral theory of canonical equations are developed and exploited in order to deduce a representation formula for the set of all solutions to the extension problem in an intuitively pleasing way. Enroute, an expository account of the forward and inverse spectral problem for canonical equations and the theory of Hilbert spaces of matrix valued entire functions is given and a number of related applications are discussed.