2019
Том 71
№ 7

# Redchuk I. K.

Articles: 3
Article (Russian)

### Separating functions, spectral theory of graphs, and locally scalar representations in Hilbert spaces

Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 36–46

We consider the connection of the separating functions $ρ_r$ with locally scalar representations of graphs and with spectral theory of graphs.

Brief Communications (Russian)

### Finite-dimensionality and growth of algebras specified by polylinearly interrelated generators

Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1435–1440

We investigate the finite-dimensionality and growth of algebras specified by a system of polylinearly interrelated generators. The results obtained are formulated in terms of a function $\rho$.

Article (Russian)

### Singular locally scalar representations of quivers in Hilbert spaces and separating functions

Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 796–809

We consider locally scalar representations of extended Dynkin graphs in Hilbert spaces. The relation between these representations and the function ρ( n ) = 1 + ( n − 1 ) / ( n + 1 ) is established. We construct a family of separating functions that generalize the function ρ and play a similar role in a broader class of graphs.