第一类不适定算子方程的解的表示  

The Expression of the Solution of the First Kind Ⅲ-Posed Operator Equation

作　　者：闫玉斌[1] 李春利[2] 

机构地区：[1]山西吕梁高等专科学校数学系,离石033000 [2]哈尔滨师范大学数学系,哈尔滨150001

出　　处：《数学物理学报（A辑）》1998年第3期264-269,共6页Acta Mathematica Scientia

基　　金：国家自然科学基金

摘　　要：该文在L2中讨论了第一类算子方程Au＝f当A-1无定义和A-1不是单值的情形下的不适定求解问题，给出了解存在的充要条件，当有解时，得到了形式解，多解时形式解就是最小范数解，并且得到了近似解表达式，给出了误差估计．In this paper, we discuss the solution of the first kind ill-posed operator equation when A-1 hasn't been defined and A-1 isn't of single value. We give the necessary and sufficient condition to the existence and uniqueness for the solution of the equation in L2. When the solution exist, we give the expression of the solution. When the equation has more than one solution, we give the minimum norm solution. Also, we obtain the expression of the approximate solution and the error estimate.

关 键 词：算子方程 最小范数解 近似解 

分 类 号：O241.8[理学—计算数学]