2018
Том 70
№ 11

All Issues

Kats G. I.

Articles: 4
Brief Communications (Russian)

Example of an annular group generated by Lee groups

Kats G. I., Palyutkin V. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1964. - 16, № 1. - pp. 99-105

Article (Russian)

Compact and discrete ring groups

Kats G. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1962. - 14, № 3. - pp. 260-270

Ring groups were introduced in note [1] as a generalization of uni-modular groups. In the present note an analogy of Pontrygin's duality theorem for compact and discrete groups is established for ring groups.

Article (Russian)

Spectral exp nsion of self-conjoint operators on generalized elements of a Hilbert space

Kats G. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1961. - 13, № 4. - pp. 13-33

The author discusses spectral expansions of generalized eigen-elements belonging to systems derived in the article (Ukrainian Mathematical Journal, vol. 12, N 1, 1960). The necessary and sufficient condition of the possibility of such expansions was obtained. Some generalizations are discussed, as well as a supplement to the estimate of the growth of eigen-functions and the interpretation of «eigen-subspaces» of self-adjoint operators.

Article (Russian)

Distributions on a Hilbert Space

Kats G. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 13-24

A general construction is given of systems of distributions on a Hilbert space. Each system is constructed according to a certain operator and the resulting distributions form a normed space. A canonical representation of these systems is obtained. In a note to follow soon, this construction will be used to obtain the spectral expansions of self-adjoint operators.