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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A spectral theory of linear operators on a rigged Hilbert space is applied toSchr\"odinger operators with exponentially decaying potentials and dilationanalytic potentials. The theory of rigged Hilbert spaces provides a unifiedapproach to resonances (generalized eigenvalues) for both classes of potentialswithout using any spectral deformation techniques. Generalized eigenvalues forone dimensional Schr\"odinger operators (ordinary differential operators) areinvestigated in detail. A certain holomorphic function $\mathbb{D}(\lambda)$ isconstructed so that $\mathbb{D}(\lambda) = 0$ if and only if $\lambda $ is ageneralized eigenvalue. It is proved that $\mathbb{D}(\lambda)$ is equivalentto the analytic continuation of the Evans function. In particular, a newformulation of the Evans function and its analytic continuation is given.

A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions II: applications to Schr\"odinger operators