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Information × Registration Number 0217U007302, 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 28-12-2017 Organization Zhytomyr State University named after Ivan Franko popup.description2 We obtained in explicit form the main extention of analytic function of complex variable into infinite-dimensional algebra. By method of hypercomplex analysis we found exact solutions of certain hydrodinamic equation. We researched Fibonacci polinoms in any algebra. In the theory of hyperholomorphic functions of spatial variable we proved an upper Zygmund-type estimate for the continuity module of singular quaternion Cauchy integral on rectifiable non-regular surface in terms of the continuity module of density of the inegral and metric characteristic of the surface. For convex domains of several-dimensional complex space we obtained relation between the contour and solid continuity modules of holomorphic functions. In three-dimensional commutative Banach algebra with one-dimensional radical the sufficient conditions for existence of boundary values of hypercomplex analogue of the Cauchy-type integral are established and analogs of Sokhotski-Pltmelj formulas for them are proved. The main biharmonic problem, the biharmonic problem and corresponding for them the Schwartz-type boundary-value problem for monogenic functions taking values in biharmonic algebra are reduced to a system of Fredholm integral equations. We solved the Schwartz-type boundary-value problem for monogenic functions taking values in biharmonic algebra reducible to boundary-value problem of problem with displacement type of the plane isotropic body theory. Boundary-value problem of problem with displacement type and corresponding it the Schwartz-type boundary-value problem are reduced to a system of Fredholm integral equations and class of domains of its univocal solvability is extnded. We established the syfficient conditions for some smooth space of solutions of a system of Fredholm integral equations to be one-dimencional. New properties of random integral operators acting in the space of second-degree integrable functions of the variable are researched. We solved an open V. M. Dubinin problem about the maximum of product of interior radiuses of finite union of non-overlapping domains, containing points of the unit circle. In several-dimensional complex space we solved the problem about product of degrees of generalized conformal radiuses of non-overlapping domains with poles on the boundary of polydisk. Product Description popup.authors Бахтін Олександр Костянтинович Грищук Сергій Вікторович Дороговцев Андрій Анатолійович Плакса Сергій Анатолійович Пухтаєвич Роман Петрович Таргонська Ірина Ігорівна Шпаківський Віталій Станіславович popup.nrat_date 2020-04-02 Close