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/

Zendy Plus

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

Zendy Tools

Zendy Open

We study general (not necessarily Hamiltonian) first-order symmetric systems$J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b\rangle $ with the regularendpoint $a$. It is assumed that the deficiency indices $n_\pm(\Tmi)$ of theminimal relation $\Tmi$ satisfy $n_+(\Tmi)< n_-(\Tmi)$. We define  $\l$-depending boundary conditions which are analogs of separatedself-adjoint boundary conditions for Hamiltonian systems. With a boundary valueproblem involving such conditions we associate an exit space self-adjointextension $\wt T$ of $\Tmi$ and the $m$-function $m(\cd)$, which is an analogof the Titchmarsh-Weyl coefficient for the Hamiltonian system. By using$m$-function we obtain the eigenfunction expansion with the spectral function$\Si(\cd)$ of the minimally possible dimension and characterize the case whenspectrum of $\wt T$ is defined by $\Si(\cd)$. Moreover, we parametrize allspectral functions in terms of a Nevanlinna type boundary parameter.Application of these results to ordinary differential operators of an odd orderenables us to complete the results by Everitt and Krishna Kumar on theTitchmarsh-Weyl theory of such operators.

On eigenfunction expansions of first-order symmetric systems and ordinary differential operators of an odd order