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- W4292339202 abstract "We study general (not necessarily Hamiltonian) first-order symmetric systems $J y'-B(t)y=D(t) f(t)$ on an interval $cI=[a,brangle $ with the regular endpoint $a$. It is assumed that the deficiency indices $n_pm(Tmi)$ of the minimal relation $Tmi$ satisfy $n_+(Tmi)< n_-(Tmi)$. We define $l$-depending boundary conditions which are analogs of separated self-adjoint boundary conditions for Hamiltonian systems. With a boundary value problem involving such conditions we associate an exit space self-adjoint extension $wt T$ of $Tmi$ and the $m$-function $m(cd)$, which is an analog of 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 when spectrum of $wt T$ is defined by $Si(cd)$. Moreover, we parametrize all spectral functions in terms of a Nevanlinna type boundary parameter. Application of these results to ordinary differential operators of an odd order enables us to complete the results by Everitt and Krishna Kumar on the Titchmarsh-Weyl theory of such operators." @default.
- W4292339202 created "2022-08-19" @default.
- W4292339202 creator A5027173528 @default.
- W4292339202 date "2013-07-25" @default.
- W4292339202 modified "2023-09-29" @default.
- W4292339202 title "On eigenfunction expansions of first-order symmetric systems and ordinary differential operators of an odd order" @default.
- W4292339202 doi "https://doi.org/10.48550/arxiv.1307.6741" @default.
- W4292339202 hasPublicationYear "2013" @default.
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