Parametrization of scale-invariant self-adjoint extensions of scale-invariant symmetric operators

Authors

  • M. B. Bekker Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA
  • M. J. Bohner Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA
  • A. P. Ugolʹnikov Department of Mathematics, Odessa National Academy of Food Technologies, Odessa, Ukraine
  • H. D. Voulov Department of Mathematics and Statistics,University of Missouri-Kansas City, Kansas City, MO, USA 

DOI:

Keywords:

Symmetric operator, scale-invariant operator, self-adjoint extension, generalized resolvents

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.

Downloads

Published

2018-03-25

Issue

Vol. 24 No. 1 (2018)

Section

Articles

How to Cite

Bekker, M. B., et al. “Parametrization of Scale-Invariant Self-Adjoint Extensions of Scale-Invariant Symmetric Operators”. Methods of Functional Analysis and Topology, vol. 24, no. 1, Mar. 2018, pp. 1-15, https://zen.imath.kiev.ua/index.php/mfat/article/view/679.