A trace formula and Schmincke inequality on the half-line.

In this paper we derive a trace formula for the Schrödinger operator on the half-line. As a consequence we obtain a Schmincke type inequality with sharp constant. The main tool in our investigation is the inverse spectral Gelfand-Levitan theory, which allows us to compare two Schrödinger operators whose spectra differ by few eigenvalues. [ABSTRACT FROM AUTHOR]