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Abstract
In this paper symmetric factorization of selfadjoint rational matrix functions with constant signature on the extended real line is studied. The concepts of constant null and pole signature are introduced and studied from several points of view. It is shown that a selfadjoint rational matrix function W(λ) with constant null and pole signature admits a factorization which is minimal everywhere in the extended complex plane with the possible exception of one pre-selected real point.
*This paper was written while the first author visited the College of William and Mary.
**Partially supported by NSF grant DMS-8802836 and by the Binational United States-Israel Science Foundation.
*This paper was written while the first author visited the College of William and Mary.
**Partially supported by NSF grant DMS-8802836 and by the Binational United States-Israel Science Foundation.
Notes
*This paper was written while the first author visited the College of William and Mary.
**Partially supported by NSF grant DMS-8802836 and by the Binational United States-Israel Science Foundation.