2019
Том 71
№ 10

All Issues

Mikityuk I. V.

Articles: 3
Article (Ukrainian)

Reduction and geometric quantization

Mikityuk I. V., Prykarpatsky A. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1220–1228

A construction is created that makes it possible to geometrically quantize a reduced Hamiltonian system using the procedure of geometric quantization realized for a Hamiltonian system with symmetries (i.e., to find the discrete spectrum and the corresponding eigenfunctions, if these have been found for the initial system). The construction is used to geometrically quantize a system obtained by reduction of a Hamiltonian system that determines the geodesic flow on an $n$-dimensional sphere.

Article (Ukrainian)

Unitary representations of the generalized Virasoro current algebra

Mikityuk I. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 532-538

Article (Ukrainian)

Abelian integrals, integrable dynamic systems of the Neumann-Rosochatius type, and the Lax representation

Mikityuk I. V., Prykarpatsky A. K., Samoilenko V. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1094–1100