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Extremal problems and algebraic-analytical methods of complex and hypercomplex analysis

Work number - M 20 AWARDED

Presented Institute of Mathematics of NAS of Ukraine

Denega I.V., Zabolotnyi Ya.V., Klishchuk B.A., Shpakivskyi V.S.

The main purpose of the work is to solve a number of current problems of modern complex analysis with an emphasis on the latest trends and approaches in this field of mathematics. This work is aimed at developing issues of complex analysis, theory of analytical functions, theory of conformal mappings and their generalizations, extremal problems of the theory of analytical functions, variational, symmetrization, extremal-metric methods of analysis and their application to problems of geometric and constructive theory of functions, to the multidimensional complex analysis, to the boundary value problems of analytical functions of complex and hypercomplex variables, research of differential, local, asymptotic and boundary properties that satisfy modular estimates.

Within the framework of this work on the basis of the latest fundamental achievements in the theory of functions, complex analysis and mapping theory a number of actual problems on extremal decomposition of the complex plane are investigated. There are also found new approaches and methods to solve these problems. The obtained results open new perspectives for further research of these problems.

The work is theoretical. Its results and methods of obtaining them are used, first of all, in the study of complex and hypercomplex analysis, holomorphic dynamics, function theory, approximation theory, potential theory, mapping theory, in boundary value problems theory for equations of mathematical physics. All results are new and make a significant addition to the development of relevant areas of the complex analysis. They were presented at various international scientific conferences, schools and scientific seminars both in Ukraine and abroad.

Number of publications: 94 scientific works (34 papers - in English-language journals with impact-factor). The total number of references to publications of authors / h-index of the work, according to databases is respectively: Web of Science – 40/4, Scopus – 89/6, Google Scholar – 274/11.