Krein Orthogonal Entire Matrix Functions and Related Lyapunov Equations: A State Space Approach |
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Authors: | M A Kaashoek L Lerer I Margulis |
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Institution: | (1) Department of Mathematics, University of California, Santa Cruz, CA 95065, USA |
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Abstract: | For a class of entire matrix valued functions of exponential type new necessary and sufficient conditions are derived in order
that these functions are Krein orthogonal functions. The conditions are stated in terms of certain operator Lyapunov equations.
These equations arise by using infinite dimensional state space representations of the entire matrix functions involved. As
a corollary, using a recent operator inertia theorem, we give a new proof of the Ellis-Gohberg-Lay theorem which relates the
number of zeros of a Krein orthogonal function in the open upper half plane to the number of negative eigenvalues of the corresponding
selfadjoint convolution operator. |
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Keywords: | |
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