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Information × Registration Number 0226U002580, (0125U001337) , R & D reports Title Analytical and approximation methods in complex and hypercomplex analysis and their applications popup.stage_title Розробка методів прикладного гіперкомплексного аналізу та алгоритми оптимального відновлення Head Shpakivskyi Vitalii S., Доктор фізико-математичних наук Registration Date 27-02-2026 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description1 The purpose of the research is to develop analytical and approximation methods of real and complex analysis for the study of extremal problems of the geometric functions theory and their application to partial differential equations. Such problems will be considered, in particular, in domains with a periodic structure, i.e. when the domain contains a periodic set of holes or inclusions. The focus will be on research in the following areas: development of the problem of complex analysis, theory of conformal mappings and their generalizations, theory of recovery, theory of approximation, extremal problems of the analytic functions theory, development of variational, symmetrization, extremal-metric methods of analysis and their application to problems of geometric and constructive theory of functions, to multidimensional complex analysis, to boundary value problems of analytic functions of a complex and hypercomplex variable. popup.description2 Research report: 112 p., 5 chapters, 90 sources. GEOMETRIC THEORY OF FUNCTIONS, INTERNAL RADIUS OF A DOMAIN, ANALYTICAL FUNCTIONS, EXTREME PROBLEMS, QUADRATIC DIFFERENTIAL, INTERNAL MAPPINGS, RIEMANN BOUNDARY-END PROBLEM FOR MONOGENIC FUNCTIONS, ENTROPY NUMBERS, FAST CONSTRUCTIVE RECOVERY ALGORITHMS. The object of research is the problems of complex and hypercomplex analysis, mapping theory and approximation theory. The purpose of the work is to develop analytical and approximation methods of real and complex analysis for the study of extremal problems of geometric theory of functions and their application in partial differential equations. The paper develops an algebraic method for constructing solutions of linear partial differential equations. A method of separating transformation for extremal problems with fixed poles of the corresponding quadratic differentials is developed. A modular technique is developed for proving theorems on the asymptotic behavior of solutions of nonlinear systems of the Cauchy-Riemann-Beltrami type. A theorem on the limit behavior of the hypercomplex analogue of the Cauchy-type integral in commutative algebras is proved. Algorithms for restoring functions in normed spaces by linear and nonlinear methods are developed and a comparison of these methods is made. Theorems on local, extremal and asymptotic properties of regular homeomorphisms in the neighborhood of a fixed point of the complex plane are proved by the isoperimetric method. The obtained results and developed approaches and methods may be useful in further studies of complex and hypercomplex analysis. Product Description popup.authors Kateryna V. Pozharska Mariia V. Stefanchuk Roman P. Pukhtaievych Iryna V. Denega popup.nrat_date 2026-02-27 Close