# A. P. Ugolʹnikov

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Articles: 2

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

Methods Funct. Anal. Topology 24 (2018), no. 1, 1-15

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.

### The Helson-Szegö theorem for operator-valued weight

Methods Funct. Anal. Topology 10 (2004), no. 3, 11-16