Let $A$ be a symmetric linear relation with arbitrary deficiency indices. By using the conceptof the boundary triplet we describe exit space self-adjointextensions $\widetilde A^\tau$ of $A$ in terms of a boundary parameter $\tau$. We characterize certain geometrical properties of $\widetilde A^\tau$ and describe all $\widetilde A^\tau$ with ${\rm mul}\, \widetilde A^\tau=\{0\}$. Applying these results to general (possibly non-Hamiltonian) symmetric systems $Jy'- B(t)y=\Delta(t)y, \; t \in [a,b\rangle,$ we describe all matrix spectral functions of theminimally possible dimension such that the Parseval equality holdsfor any function $f\in L_\Delta^2([a,b \rangle)$.
Key words: Symmetric relation, exit space extension, boundary triplet, first order symmetric system, spectral function.
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Article Information
Title
On exit space extensions of symmetric operators with applications to first order symmetric systems
V. I. Mogilevskii, On exit space extensions of symmetric operators with applications to first order symmetric systems, Methods Funct. Anal. Topology 19
(2013), no. 3, 268-292.
BibTex
@article {MFAT686,
AUTHOR = {Mogilevskii, V. I.},
TITLE = {On exit space extensions of symmetric operators with applications to first order symmetric systems},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {3},
PAGES = {268-292},
ISSN = {1029-3531},
MRNUMBER = {MR3136731},
ZBLNUMBER = {1289.47046},
URL = {http://mfat.imath.kiev.ua/article/?id=686},
}
