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Information × Registration Number 0214U006347, 0112U000374 , R & D reports Title Monogenic and hyperholomorphic functions in finite-dimensional algebras and their application to the boundary problems of mathematical physics popup.stage_title Head Gerus Oleg Fedorovych, Кандидат фізико-математичних наук Registration Date 11-03-2014 Organization Zhytomyr State University named after Ivan Franko popup.description2 A constructive description of monogenic functions in a three-dimension harmonic algebra with one-dimensional radical in terms of analytic functions of complex variable is established. A new definition of hyperholomorphic function of spatial variable is introduced. An analog of the Cauchy theorem for hyperholomorphic quaternionic functions is proved. Formulas for boundary values of a hypercomplex Cauchy-type integral are proved and logarithmic residue for monogenic functions with values in a three-dimensional harmonic algebra with two-dimensional radical is calculated. Boundary problems of the Schwartz-type for a circle and for a half-plane associated with the main biharmonic problem are solved in the explicit form. Conditions of monogenety of functions in infinite-dimensional topological vectorial spaces with commutative multipication are established. Some quaternionical identities are generalized onto algebras Kelly-Dixon. Properties of Fibonacci quaternions are investigated. Product Description popup.authors Грищук Саргій Вікторович Плакса Сергій Анатолійович Пухтаєвич Роман Петрович Шпаківський Віталій Станіславович popup.nrat_date 2020-04-02 Close