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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Linear differential-difference operators and their adjoints


Author: David K. Hughes
Journal: Proc. Amer. Math. Soc. 26 (1970), 408-414
MSC: Primary 34K10
DOI: https://doi.org/10.1090/S0002-9939-1970-0412557-6
MathSciNet review: 0412557
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Abstract: The formal adjoint for a first order matrix differential-difference operator is shown to be a true Hilbert space adjoint, and conditions under which such operators are selfadjoint (in a Hilbert space sense) are derived. Differential-difference operators whose domains are defined by a given initial function cannot be selfadjoint, whereas certain operators whose domains are defined only by conditions at the endpoints of an interval can be selfadjoint.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0412557-6
Keywords: Differential-difference operators, differential-difference equations, functional-differential equations, formal adjoint, Hilbert space adjoint, selfadjoint differential operator
Article copyright: © Copyright 1970 American Mathematical Society