2019
Том 71
№ 9

All Issues

Lukyanova E. A.

Articles: 3
Article (Russian)

Pseudoanalyticity of continuous functions with the ?-preservation of angles

Bondar A. V., Lukyanova E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1051–1057

The following theorem is proved: Every continuous function satisfying the condition $K'_{\sigma}$ is pseudo-analytic. The condition $K'_{\sigma}$ is a generalization of the Men'shov condition, well known in the theory of analytic functions.

Article (Russian)

On pseudoanalyticity of continuous functions with constant $σ$-extension

Bondar A. V., Lukyanova E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 459–465

The theorem on pseudoanalyticity of continuous functions with constant $σ$-extension is proved; this is an analog of the well known results due to Bohr, Rademacher, Men'shov, and Trokhimchuk concerning the analyticity of functions with constant extension.

Article (Russian)

On the structure of sets of $ σ$-monogeneity for continuous functions

Bondar A. V., Lukyanova E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 226–232

The notion of the sets of σ-monogeneity for continuous functions is introduced which makes it possible to study pseudo-analytic properties of these functions. The theorem on the structure of these sets is proved.