Journal of Operator Theory

Volume 95, Issue 2, Spring 2026 pp. 581-612.

Boundary value problems for adjoint pairs of operators

Authors: Jussi Behrndt
Author institution: Institut fuer Angewandte Mathematik, Technische Universitaet Graz, Steyrergasse 30, 8010 Graz, Austria

Summary: The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators in Hilbert spaces is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of the corresponding abstract Titchmarsh-Weyl $M$-functions sufficient conditions for the unique solvability of the related boundary value problems are obtained and the solutions are expressed via Krein-type resolvent formulae. The abstract theory developed in this manuscript can be applied to a large class of elliptic differential operators.

DOI: http://dx.doi.org/10.7900/jot.2024oct21.2491
Keywords: adjoint pair, dual pair, boundary value problem, boundary triple, Weyl function

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