Abstract
On a Hilbert space $\frak H$, we consider a symmetric scale-invariant operator with equal defect numbers. It is assumed that the operator has at least one scale-invariant self-adjoint extension in $ \frak H$. We prove that there is a one-to-one correspondence between (generalized) resolvents of scale-invariant extensions and solutions of some functional equation. Two examples of Dirac-type operators are considered.
Key words: Symmetric operator, scale-invariant operator, self-adjoint extension, generalized resolvents.
Full Text
Article Information
| Title | Parametrization of scale-invariant self-adjoint extensions of scale-invariant symmetric operators |
| Source | Methods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 1-15 |
| MathSciNet |
MR3783813 |
| Milestones | Received 11/08/2017; Revised 03/11/2017 |
| Copyright | The Author(s) 2018 (CC BY-SA) |
Authors Information
Miron B. Bekker
Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA
Martin J. Bohner
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA
Alexander P. Ugolʹnikov
Department of Mathematics, Odessa National Academy of Food Technologies, Odessa, Ukraine
Hristo Voulov
Department of Mathematics and Statistics,University of Missouri-Kansas City, Kansas City, MO, USA
Citation Example
Miron B. Bekker, Martin J. Bohner, Alexander P. Ugolʹnikov, and Hristo Voulov, Parametrization of scale-invariant self-adjoint extensions of scale-invariant symmetric operators, Methods Funct. Anal. Topology 24
(2018), no. 1, 1-15.
BibTex
@article {MFAT1020,
AUTHOR = {Miron B. Bekker and Martin J. Bohner and Alexander P. Ugolʹnikov and Hristo Voulov},
TITLE = {Parametrization of scale-invariant self-adjoint extensions of scale-invariant symmetric operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {1},
PAGES = {1-15},
ISSN = {1029-3531},
MRNUMBER = {MR3783813},
URL = {http://mfat.imath.kiev.ua/article/?id=1020},
}
