Linear differential-difference operators and their adjoints

Hughes, David K.

doi:10.1090/S0002-9939-1970-0412557-6

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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