Search academic texts

Information × Registration Number 0210U003802, 0108U009037 , R & D reports Title Algebraic equations in hypercomplex algebras and boundary problems for hyperholomorphic functions and potentials popup.stage_title Head Tamrazov Promarz Melikovich, Registration Date 09-03-2010 Organization Zhytomyr State University named after Ivan Franko popup.description2 There obtained a constructive description of monogenic functions taking values in a commutative Banach algebra and defined in the biharmonic plane. There described all monogenic functions of the biharmonic variable taking values in the ideal of the algebra. Point spectrums of spatial quaternion singular Cauchy operator and of two real integral operators being its component parts have been investigated. The Gateaux differetiable functions defined in an infinite dimensional commutative algebra taking values in the algebra have been investigated. There cited exampled associated with twodimentional and threedimentional Laplace equations and with the twodimentional biharmonic equation. There proved that each quadratic quaternion equation with nonsplit squares is a quasispherical equation. There established sufficient conditions for a given quadratic quaternion equation, having decomposable onto linear factors the left-side part, to be a multiquasispherical equation. For monogenic functions analogues of the Cauchy theorem for the curvelinear integral, of the integral Cauchy formula, of the Morera theorem and the power series expansion formula have been proved. The equivalence of different definitions of monogenic functions have been established. Product Description popup.authors Герус Олег Федорович Грищук Сергій Вікторович Мержеєвський Дмитро Арнольдович Плакса Сергій Анатолійович Погоруй Анатолій Олександрович Прилипко Ольга Володимирівна Шпаківський Віталій Станіславович popup.nrat_date 2020-04-02 Close