2019
Том 71
№ 10

All Issues

Gerus O. F.

Articles: 7
Article (Ukrainian)

On hyperholomorphic functions of the space variable

Gerus O. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 459-465

For quaternionic-differentiable functions of a spatial variable, we prove a theorem on an integral over a closed surface. This theorem is an analog of the Cauchy theorem from complex analysis.

Brief Communications (Ukrainian)

An estimate for the modulus of continuity of a quaternion singular Cauchy integral

Gerus O. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1428–1435

We establish an upper bound for the modulus of continuity of a quaternion singular Cauchy integral in terms of the modulus of continuity of the integrand and a metric characteristic of a curve.

Article (Russian)

Estimates for the modulus of a Cauchy-type integral and its derivatives

Gerus O. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 732–743

In a domain bounded by a closed rectifiable Jordan curve, we obtain estimates for the modulus of a Cauchy-type integral and its derivatives in terms of the contour moduli of smoothness of the integrand and a metric characteristic of the curve.

Article (Russian)

On the modulus of continuity of solid derivatives of a Cauchy-type integral

Gerus O. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 476–484

We establish sufficient conditions for the existence of solid derivatives of a continuous extension of a Cauchy-type integral onto the closure of a domain and obtain an estimate for the moduli of continuity of these derivatives. We prove that the Newton-Leibniz formula is true for certain classes of Jordan rectifiable curves.

Article (Russian)

Estimate of the modulus of continuity of a cauchy-type integral in a domain and on its boundary

Gerus O. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1321-1328

We estimate the modulus of continuity of a Cauchy-type integral in a closed domain and its limit values on the boundary in the case where the boundary of the domain is an arbitrary closed rectifiable Jordan curve.

Article (Ukrainian)

Some estimates of smoothness moduli of Cauchy integrals

Gerus O. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 5. - pp. 594–601

Article (Ukrainian)

Finite-dimensional smoothness of Cauchy-type integrals

Gerus O. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 5. - pp. 642–646