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Parameterization of the M(λ) function for a Hamiltonian system of limit circle type

Published online by Cambridge University Press:  14 November 2011

D. B. Hinton
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37916, U.S.A.
J. K. Shaw
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute, Blacksburg, VA 24061, U.S.A.

Synopsis

The authors continue their study of Titchmarch-Weyl matrix M(λ) functions for linear Hamiltonian systems. A representation for the M(λ) function is obtained in the case where the system is limit circle, or maximum deficiency index, type. The representation reduces, in a special case, to a parameterization for scalar m-coefficients due to C. T. Fulton. A proof that matrix M(λ) functions are meromorphic in the limit circle case is given.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1983

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