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 Gelfand triplet for the Hamiltonian H of the Friedrichs model on R withfinite-dimensional multiplicity space K, is constructed such that exactly theresonances (poles of the inverse of the Livsic-matrix) are (generalized)eigenvalues of H. The corresponding eigen-antilinearforms are calculatedexplicitly. Using the wave matrices for the wave (Moller) operators thecorresponding eigen-antilinearforms on the Schwartz space S for the unperturbedHamiltonian are also calculated. It turns out that they are of pure Dirac typeand can be characterized by their corresponding Gamov vector, which is uniquelydetermined by restriction of S to the intersection of S with the Hardy space ofthe upper half plane. Simultaneously this restriction yields a truncation ofthe generalized evolution to the well-known decay semigroup of the Toeplitztype for the positive half line on the Hardy space. That is: exactly thosepre-Gamov vectors (eigenvectors of the decay semigroup) have an extension to ageneralized eigenvector of H if the eigenvalue is a resonance and if themultiplicity parameter k is from that subspace of K which is uniquelydetermined by its corresponding Dirac type antilinearform.Comment: 16 page

GENERALIZED EIGENVECTORS FOR RESONANCES IN THE FRIEDRICHS MODEL AND THEIR ASSOCIATED GAMOV VECTORS