Half-inverse problems on the finite interval (Q2738850)

Let \(S:=\{\lambda_n\}\) be the spectrum of the boundary value problem NEWLINE\[NEWLINE -y''+p(x)y=\lambda y,\quad 0<x<1, \qquad y(0)=y(1)=0, NEWLINE\]NEWLINE where \(p(x)\) is real and continuous. Using the transformation operator method, the author provides a solution to the following inverse problems: NEWLINENEWLINENEWLINE1) given the spectrum \(S\) and \(p(x)\), \(x\in [0,1/2],\) construct \(p(x)\), \(x\in [1/2,1]\); NEWLINENEWLINENEWLINE2) given the spectrum \(S\) and the function \(p(x)-p(1-x)\), construct \(p(x)\), \(x\in [0,1]\).