Krein's Resolvent Formula for Self-Adjoint Extensions of Symmetric Second Order Elliptic Differential Operators

Abstract

Given a symmetric, semi-bounded, second order elliptic differential operator on a bounded domain with $C^{1,1}$ boundary, we provide a Krein-type formula for the resolvent difference between its Friedrichs extension and an arbitrary self-adjoint one.

Final version, to appear in J. Phys. A: Math. Theor

References in corpus (4)

• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• First order operators and boundary triples
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
• Self-adjoint Extensions of Restrictions

Cited by in corpus (2)

• Krein resolvent formulas for elliptic boundary problems in nonsmooth domains
• The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum