Formally self-adjoint quasi-differential operators and boundary value problems

Abstract

We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique are then used to describe all maximal dissipative, accumulative and self-adjoint extensions of the associated minimal operator and its generalized resolvents in terms of the boundary conditions. Some specific classes are considered in greater detail.

Extended and revised version. Results concerning regularization by quasi-derivatives of formal differential operators with distributional coefficients were added. 13 pages

References in corpus (2)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials

Cited by in corpus (5)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• Remarks on Schrödinger operators with singular matrix potentials
• A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems
• Sturm-Liouville operators with matrix distributional coefficients
• The Krein-von Neumann Extension of a Regular Even Order Quasi-Differential Operator