2019
Том 71
№ 7

All Issues

Mel'nik Yu. I.

Articles: 14
Article (Ukrainian)

On the rate of convergence of double series of exponents representing regular functions on products of convex polygons

Mel'nik Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1271–1274

Estimates exact in order are obtained in the uniform and integral metrics for the deviation of partial sums of double series of exponents that represent functions which are regular on products of convex polygons and either continuous on a product of closed polygons or belonging to the Smirnov class.

Article (Ukrainian)

On divergence of series of exponents representing functions regular in convex polygons

Mel'nik Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 443–445

We prove that, on a convex polygon, there exist functions from the Smirnov classE whose series of exponents diverge in the metric of the spaceE. Similar facts are established for the convergence almost everywhere on the boundary of a polygon, for the uniform convergence on a closed polygon, and for the pointwise convergence at noncorner points of the boundary.

Article (Ukrainian)

Inverse theorems for approximation of functions regular in convex polygons by exponential polynomials in the integral metric

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 751-757

Article (Ukrainian)

Direct theorems for the approximation of functions, regular in convex polygons, by exponential polynomials in the integral metric

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 5. - pp. 584-591

Article (Ukrainian)

Approximation of functions regular in convex polygons by exponential polynomials

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 446–452

Article (Ukrainian)

Rate of convergence of exponential series representing functions regular in convex polygons

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 719–722

Article (Ukrainian)

Absolute convergence of series of exponents that represent regular functions in convex polygons

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 6. - pp. 772–782

Article (Ukrainian)

Uniqueness of expansion of a function, regular in a convex polygon, into a series of exponential functions

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 2. - pp. 217-219

Article (Ukrainian)

A method of integral equations and the Riemann boundary problem

Mel'nik Yu. I., Podlipenko S. N., Podlipenko Yu. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 382–385

Article (Ukrainian)

Approximate solution of integral equations in potential theory

Mel'nik Yu. I., Podlipenko S. N., Podlipenko Yu. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 385–391

Article (Ukrainian)

Dirichlet series of functions, regular in convex polygons

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 837–843

Article (Ukrainian)

A universal system of exponentials

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 2. - pp. 192–196

Article (Ukrainian)

Representation of regular functions by series of Mittag-Leffler functions in a closed disk

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 1. - pp. 114–120

Article (Ukrainian)

Representation of regular functions by Dirichlet series in closed convex polygons

Mel'nik Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 6. - pp. 826–830