The Properties And Iterative Approximation Of Cauchy-type Integral Operators Associated With The Helmholtz Equation And The Time-harmonic Maxwell Equations

The theory of Cauchy-type integral operators has important applications in different fields of modern mathematics and physics,which attracts a large number of famous schol-ars at home and abroad to make further research on it.Thus the Cauchy-type integral operator have formed a relatively complete theoretical system in the real and complex analysis.In quaternionic analysis,the study of the Cauchy-type integral operator associ-ated with the regular function is more perfect.However the research on Cauchy-type in-tegral operators associated with the Helmholtz equation and the Time-harmonic Maxwell equations is relatively less.Therefore,by using the method of quaternionic analysis.This paper studies the properties and iterative approximation of Cauchy-type integral opera-tors associated with the Helmholtz equation and the Time-harmonic Maxwell equations.In the first chapter,some preparatory knowledge and several important lemmas are given.In the second chapter,the H(?)lder continuity of the Cauchy-type integral operator related to the Helmholtz equation is first discussed in the following three cases two points are on the boundary;one is on the boundary and the other is inside the region(outside the region);two points are inside the region(outside the region).And the relationship between the norm of Soa[f]and f is discussed.Based on these results,the existence and iterative approximation of the fixed point of the singular integral operators (?)? are studied.In the third chapter,the Cauchy-type integral operator related to the N matrix operator is introduced.And by using the conclusion of the second chapter,the H(?)lder continuity is proved in the above three cases respectively.In the fourth chapter,the Cauchy-type integral operator related to the Time-harmonic Maxwell equations is introduced.The relationship between it and the Cauchy-type inte-gral operator related to the N matrix operator is studied.By using the conclusion of the third chapter,their H(?)lder continuity under three cases are given respectively.