Extremal norms of the potentials recovered from inverse Dirichlet problems (Q2807465)

It is known that any given distribution of eigenvalues satisfying the required asymptotics can be associated with a family of Sturm-Liouville operators of the form NEWLINE\[NEWLINEL_{q}(y)=-y''(x)+q\left( x\right) y(x) NEWLINE\]NEWLINE with \(y(0)=y(1)=0\). Adding the norming constants will yield a unique potential \(q\). The authors look for the smallest possible \(q\) associated with all the isospectral operators \(L_{q}\) sharing the same given spectrum. The method uses inequalities of Lyapunov type.