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Equivalence, adjoints and symmetry of quasi-differential expressions with matrix-valued coefficients and polynomials in them

Published online by Cambridge University Press:  14 November 2011

Hilbert Frentzen
Hilbert Frentzen
Affiliation:
Fachbereich 6, Mathematik, Universitat Essen-GHS, D-4300 Essen 1, B.R.D.
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Synopsis

Quasi-differential expressions with matrix-valued coefficients, which generalize those of Shin and Zettl, are considered with regard to equivalence, adjoints and symmetry. The characterization results imply that in the scalar case the class of quasi-differential expressions considered here coincides with that of Shin and is equivalent to that of Zettl. Furthermore polynomials in quasi-differential expressions are defined as expressions of the same kind and shown to coincide with the usual ones. Finally it is indicated that the known general results for the deficiency indices carry over to quasi-differential expressions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 123 - 146
Copyright
Copyright © Royal Society of Edinburgh 1982

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