2019
Том 71
№ 6

All Issues

Abdullayev G. A.

Articles: 3
Article (Russian)

Bernstein – Walsh-type polynomial inequalities in domains bounded by piecewise asymptotically conformal curve with nonzero inner angles in the Bergman space

Abdullayev G. A., Abdullayev F. G., Şimşek D.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 5. - pp. 583-595

UDC 517.5
We continue the investigation of the order of growth of the modulus of an arbitrary algebraic polynomial in the Bergman weight space, where the contour and weight functions have certain singularities. In particular, we deduce a Bernstein– Walsh-type pointwise estimate for algebraic polynomials in unbounded domains with a piecewise asymptotically conformal curve with nonzero inner angles in the Bergman weight space.

Article (English)

Polynomial inequalities in quasidisks on weighted Bergman space

Abdullayev G. A., Abdullayev F. G., Tunç E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 582-598

We continue studying on the Nikol’skii and Bernstein –Walsh type estimations for complex algebraic polynomials in the bounded and unbounded quasidisks on the weighted Bergman space.

Article (English)

On Some Properties of Orthogonal Polynomials over an Area in Domains of the Complex Plane. III

Abdullayev G. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 12. - pp. 1588-1599

We study polynomials of higher order orthogonal with weight over domains under the condition that the boundary and weight functions have singularities and do not satisfy the conditions of interference.