Variations on a Theme of Jost and Pais

Simple item page
dc.creatorGesztesy, Fritz
dc.creatorMitrea, Marius
dc.creatorZinchenko, Maxim
dc.date2007-05-24
dc.date.accessioned2026-07-07T08:03:04Z
dc.date.available2026-07-07T08:03:04Z
dc.descriptionWe explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension the half-line is replaced by an open set $Ω\subset\bbR^n$, $n\in\bbN$, $n\geq 2$, where $Ω$ has a compact, nonempty boundary $\partialΩ$ satisfying certain regularity conditions. Our variant involves ratios of perturbation determinants corresponding to Dirichlet and Neumann boundary conditions on $\partialΩ$ and invokes the corresponding Dirichlet-to-Neumann map. As a result, we succeed in reducing a certain ratio of modified Fredholm perturbation determinants associated with operators in $L^2(Ω; d^n x)$, $n\in\bbN$, to modified Fredholm determinants associated with operators in $L^2(\partialΩ; d^{n-1}σ)$, $n\geq 2$. Applications involving the Birman-Schwinger principle and eigenvalue counting functions are discussed.
dc.description40 pages. To appear in J. Funct. Anal
dc.identifierhttps://arxiv.org/abs/0705.3510
dc.identifierhttp://arxiv.org/abs/0705.3510
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129445
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subjectPrimary: 47B10, 47G10, Secondary: 34B27, 34L40.
dc.titleVariations on a Theme of Jost and Pais
dc.typetext

Files

Collections

arXiv