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The inverse nodal problem for Hill's equation

We study the inverse nodal problem for Hill's equation. In particular, we solve the uniqueness, reconstruction and stability problems using the nodal set of periodic (or anti-periodic) eigenfunctions. Furthermore, we show that the space of periodic potential functions q normalized by ∫10q = 0 is homeomorphic to the partition set of the space of quasinodal sequences. Our method is to make a translation so that the periodic (or anti-periodic) problem is reduced to a Dirichlet problem.