Resolvents of self-adjoint extensions with mixed boundary conditions

2004/12/31 by Konstantin Pankrashkin · 47 citations
Computer Science · Mathematics · Physics and Astronomy · #Banach space #Boundary (topology) #Boundary value problem #Hilbert space #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Pure mathematics #Quantum #Quantum mechanics #Resolvent #Resolvent formalism #Self-adjoint operator #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP #msc:34B05 #msc:47A06 #msc:47A10

paper · pdf · doi:10.1016/s0034-4877(06)80048-0

published in Reports on Mathematical Physics 58(2), 207-221 (Elsevier BV) · 15 pages, rewritten almost completely

arxiv created 2006/03/30 · openalex publication_date 2006/10/01 · arxiv updated 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove a variant of Krein's resolvent formula expressing the resolvents of self-adjoint extensions through the associated boundary conditions. Applications to solvable quantum-mechanical problems are discussed.

Citations

• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• Kirchhoff's rule for quantum wires
• A remark on Krein's resolvent formula and boundary conditions
• On-diagonal singularities of the Green functions for Schrödinger operators
• The generalized point interaction in one dimension
• Characteristic class entering in quantization conditions