A spectral shift function for Schrödinger operators with singular interactions

2017/10/10 by Jussi Behrndt, Fritz Gesztesy, Behrndt, Jussi +3
Mathematics · #35J10 #35J15 #35P20 #35P25 #47A10 #47A40 #47A55 #47B10 #47B25 (Primary) #47F05 #81Q10 (Secondary) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1710.03367

openalex publication_date 2017/10/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

For the pair \-Δ, -Δ-αδ_C\ of self-adjoint Schrödinger operators in L²(ℝⁿ) a spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps. Here δ_\calC denotes a singular δ-potential which is supported on a smooth compact hypersurface C⊂ℝⁿ and α is a real-valued function on C.

Related

• Spectral shift functions and Dirichlet-to-Neumann maps
• Singular Schrödinger operators with prescribed spectral properties
• Singular spectral shift function for Schrödinger operators
• Spectral shift for relative Schatten class perturbations
• Spectral theory for Schrödinger operators with δ-interactions supported on curves in ℝ³