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Information × Registration Number 0216U007501, 0116U001528 , R & D reports Title Monogenic Functions in Banach Algebras and Boundary Problems of Analysis and Mathematical Physics popup.stage_title Head Gerus Oleg Fedorovych, Кандидат фізико-математичних наук Registration Date 20-12-2016 Organization Zhytomyr State University named after Ivan Franko popup.description2 For monogenic functions in any commutative algebra we proved analogues of the Cauchy integral theorem and the Cauchy integral formula. We proved an analogue of the Morera's theorem. We constructed a hypercomplex representation of analytic solutions of certain hydrodinamic equation. We proved a spatial analogue of the Cauchy integral theorem for quaternionic hyperholomorphic functions of spatial variable. We obtained a constructive description of the whyle monogenic functions in any finite-dimensional commutative associative algebra over the field of complex numbers in terms of holomorphic functions of complex variable. We obtained a constructive description of G-monogenic mapping acting to the algebra of complex quaternions in terms of analytic functions of complex variable. We proved analogues of classic integral theorems for G-monogenic mappings acting to the algebra of complex quaternions. We proved equivalence of different definitions of G-monogenic mapping. We calculated logaritmic residue of monogenic functions in three-dimensional commutative associative complex Banach algebra with one-dimensional radical. For domains with boundaries from more wide classes when previously considered in two-dimensional elasticity theory, basic biharmonic problem and correspondent Schwarz-type boundary-value problem for monogenic functions acting to biharmonic algebra was reduced to Fredholm integral equations system. For canonical domains we found solutions of Schwarz-type problem associate with a shifted boundary-value problem for elastic isotropic environment in the form of hypercomplex Schwarz integrals.5481 Product Description popup.authors Грищук Сергій Вікторович Кузьменко Тетяна Сергіївна Плакса Сергій Анатолійович Пухтаєвич Роман Петрович Шпаківський Віталій Станіславович popup.nrat_date 2020-04-02 Close