On the relative heat invariants of the Dirichlet-to-Neumann operators associated with Schrödinger operators

In this paper we study the relative heat invariants of the Dirichlet-to-Neumann operators \(\Lambda _V\) associated with Schrodinger operators. Using Seeley’s method, we will calculate the first several relative heat trace invariants explicitly, and then give the general structure of the first n relative heat invariants. As applications, we will prove that a number of properties of the potential V are determined by the spectrum of \(\Lambda _V\).