This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multipl...This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multiple power series expansions and an iterative computation method to solve a kind of integro-differential equation. We introduce a symmetrized topology product area which is called a bicylinder. We expand functions and derivatives of them to power series. Moreover we obtain unknown functions by comparing coefficients of the series on both sides of equations. We express the approximation solutions by a regular product of matrixes.展开更多
It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is co...It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is complexity,the Jacobian determinant included in the kernel is expanded for making clearly the expression of the kernel.Moreover,one differential operator is utilized for setting up relations between integrals with higher and usual orders.The work also concerns the convergent properties of the integral.In order to study Hadamard principal value and composite formula of this integral,finite and divergent parts will be estimated and separated.As an application,solvability of the system of integral equations with higher order singularity kernel is discussed.展开更多
基金supported by the National Natural Science Foundation of China(11771357,11171277)the Fundamental Research Funds for the Central Universities of Xiamen University(2010121002)the Science Foundation of Fujian province of China(S0850029,2008J0206)
文摘This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multiple power series expansions and an iterative computation method to solve a kind of integro-differential equation. We introduce a symmetrized topology product area which is called a bicylinder. We expand functions and derivatives of them to power series. Moreover we obtain unknown functions by comparing coefficients of the series on both sides of equations. We express the approximation solutions by a regular product of matrixes.
基金Supported by the National Natural Science Foundation of China(Grant No.11771357)。
文摘It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is complexity,the Jacobian determinant included in the kernel is expanded for making clearly the expression of the kernel.Moreover,one differential operator is utilized for setting up relations between integrals with higher and usual orders.The work also concerns the convergent properties of the integral.In order to study Hadamard principal value and composite formula of this integral,finite and divergent parts will be estimated and separated.As an application,solvability of the system of integral equations with higher order singularity kernel is discussed.
