Open Access

On exit space extensions of symmetric operators with applications to first order symmetric systems

     Article (.pdf)

Abstract

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.


Full Text





Article Information

TitleOn exit space extensions of symmetric operators with applications to first order symmetric systems
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 3, 268-292
MathSciNet MR3136731
zbMATH 1289.47046
MilestonesReceived 21/03/2013; Revised 02/04/2013
CopyrightThe Author(s) 2013 (CC BY-SA)

Authors Information

V. I. Mogilevskii
Department of Mathematical Analysis, Lugans'k Taras Shevchenko National University, 2 Oboronna, Lugans'k, 91011, Ukraine 


Citation Example

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},
}


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar


Export article

Save to Mendeley


All Issues