English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider Dirichlet-to-Neumann maps associated with (not necessarilyself-adjoint) Schrodinger operators describing nonlocal interactions in$L^2(\Omega; d^n x)$, $n\geq 2$, where $\Omega$ is an open set with a compact,nonempty boundary satisfying certain regularity conditions. As an applicationwe describe a reduction of a certain ratio of Fredholm perturbationdeterminants associated with operators in $L^2(\Omega; d^n x)$ to Fredholmperturbation determinants associated with operators in $L^2(\partial\Omega;d^{n-1}\sigma)$. This leads to an extension of a variant of a celebratedformula due to Jost and Pais, which reduces the Fredholm perturbationdeterminant associated with a Schr\"odinger operator on the half-line$(0,\infty)$, in the case of local interactions, to a Wronski determinant ofappropriate distributional solutions of the underlying Schrodinger equation.

On Dirichlet-to-Neumann Maps, Nonlocal Interactions, and Some Applications to Fredholm Determinants