第一类不适定算子方程的解的表示

Abstract

Abstract: 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.

Key words: Operator equation, Minimum norm solution, Approximate solution

Yan Yubin, Li Chunli. The Expression of the Solution of the First Kind Ⅲ-Posed Operator Equation[J].Acta mathematica scientia,Series A, 1998, 18(3): 264-269.

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

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