Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators

2008/04/30 by Andrea Posilicano, Luca Raimondi · 66 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Banach space #Boundary value problem #Bounded function #Differential Equations and Boundary Problems #Differential operator #Domain (mathematical analysis) #Elliptic operator #Finite-rank operator #Hilbert space #Mathematical analysis #Mathematics #Operator (biology) #Order (exchange) #Pure mathematics #Resolvent #Resolvent formalism #Self-adjoint operator #Semi-elliptic operator #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP

paper · pdf · doi:10.1088/1751-8113/42/1/015204

published in Journal of Physics A Mathematical and Theoretical 42(1), 015204 (Institute of Physics) · Final version, to appear in J. Phys. A: Math. Theor

arxiv created 2008/11/02 · openalex publication_date 2008/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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

Citations

• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
• Self-Adjoint Extensions by Additive Perturbations
• Self-adjoint Extensions of Restrictions
• Boundary value problems for elliptic partial differential operators on bounded domains

Cited by

• Spectral theory for perturbed Krein Laplacians in nonsmooth domains
• Markovian extensions of symmetric second order elliptic differential operators