Extreme problem for a mosaic system of points

2020 ◽  
Vol 17 (3) ◽  
pp. 437-447
Author(s):  
Andrii Targonskii ◽  
Iryna Targonskaya
Keyword(s):  
Complex Variable ◽  
Geometric Theory ◽  
Nonoverlapping Domains ◽  
Extreme Problem

In the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise nonoverlapping domains. This direction is called extreme problems in classes of pairwise nonoverlapping domains. One of the problems of this type is considered in the present work.

Problem on extremal decomposition of the complex plane with free poles

2020 ◽  
Vol 17 (1) ◽  
pp. 3-29
Author(s):  
Aleksandr Bakhtin ◽  
Liudmyla Vyhivska
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Geometric Theory ◽  
Extremal Decomposition ◽  
Overlapping Domains

We consider the well-known problem of the geometric theory of functions of a complex variable on non-overlapping domains with free poles on radial systems. The main results of the present work strengthen and generalize several known results for this problem.

scholarly journals Estimates of the inner radii of non-overlapping domains

2019 ◽  
Vol 16 (1) ◽  
pp. 46-56
Author(s):  
Iryna Denega
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Geometric Theory ◽  
Extremal Problems ◽  
Improved Method ◽  
Extremal Decomposition ◽  
Overlapping Domains

Some extremal problems of the geometric theory of functions of a complex variable related to the estimates of functionals defined on systems of non-overlapping domains are considered. Till now, many such problems have not been solved, though some partial solutions are available. In the paper, the improved method is proposed for solving the problems on extremal decomposition of the complex plane. The main results generalize and strengthen some known results in the theory of non-overlapping domains with free poles to the case of an arbitrary arrangement of systems of points on the complex plane.

scholarly journals Extreme problem for partially nonoverlapping domains on a Riemann sphere

2018 ◽  
Vol 235 (1) ◽  
pp. 74-80 ◽  
Author(s):  
Andrei L. Targonskii ◽  
Irina I. Targonskaya
Keyword(s):  
Riemann Sphere ◽  
Nonoverlapping Domains ◽  
Extreme Problem

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

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