V. I. Mogilevskii Department of Mathematical Analysis and Informatics, Poltava National V. G. Korolenko Pedagogical University, 2 Ostrogradski str., Poltava, 36000, Ukraine
Let $\mathfrak H$ be a Hilbert space and let $A$ be a symmetric linear relation (in particular, a nondensely defined operator) in $\mathfrak H$. By using the concept of a boundary triplet for $A^*$ we characterize symmetric extensions $\widetilde A\supset A$ preserving the multivalued part of $A$. Such a characterization is given in terms of an abstract boundary parameter and the Weyl function of the boundary triplet. Application of these results to the Hamiltonian system $Jy'-B(t)y=\lambda\Delta(t) y$ enabled us to describe its matrix solutions generating the generalized Fourier transform with the nonempty set of respective spectral functions.
V. I. Mogilevskii Department of Mathematical Analysis and Informatics, Poltava National V. G. Korolenko Pedagogical University, 2 Ostrogradski str., Poltava, 36000, Ukraine
V. I. Mogilevskii, Symmetric extensions of symmetric linear relations
(operators) preserving the multivalued part, Methods Funct. Anal. Topology 24
(2018), no. 2, 152-177.
BibTex
@article {MFAT1055,
AUTHOR = {Mogilevskii, V. I.},
TITLE = {Symmetric extensions of symmetric linear relations
(operators) preserving the multivalued part},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {2},
PAGES = {152-177},
ISSN = {1029-3531},
MRNUMBER = {MR3827126},
URL = {http://mfat.imath.kiev.ua/article/?id=1055},
}
