2010/02/01 by Fritz Gesztesy, Marius Mitrea, Gesztesy, Fritz +3
Computer Science · Mathematics · Physics and Astronomy · #34B27 #34L40. #47B10 #47G10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34B27 #msc:34L40. #msc:47B10 #msc:47G10
paper · pdf · doi:10.48550/arxiv.1002.0389
20 pages
openalex publication_date 2010/02/01 · arxiv created 2010/02/03 · arxiv updated 2010/02/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrodinger operators in L2(Ω; dn x), n=2,3, where Ω is an open set with a compact, nonempty boundary satisfying certain regularity conditions. As an application we describe a reduction of a certain ratio of modified Fredholm perturbation determinants associated with operators in L2(Ω; dn x) to modified Fredholm perturbation determinants associated with operators in L2(∂Ω; dn-1σ), n=2,3. This leads to a two- and three-dimensional extension of a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with a Schrodinger operator on the half-line (0,∞) to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrodinger equation.