On a Hilbert space 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 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.
M. B. Bekker et al., "Parametrization of Scale-Invariant Self-Adjoint Extensions of Scale-Invariant Symmetric Operators," Methods of Functional Analysis and Topology, vol. 24, no. 1, pp. 1-15, Institute of Mathematics NAS of Ukraine, Jan 2018.
Mathematics and Statistics
Keywords and Phrases
Generalized resolvents; Scale-invariant operator; Self-adjoint extension; Symmetric operator
International Standard Serial Number (ISSN)
Article - Journal
01 Jan 2018