The boundary control approach to the Titchmarsh-Weyl $m-$function

Abstract

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the $A-$amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl $m-$function associated with the Schrödinger operator $H=-{\partial }_x^2+q\left(x\right)$ on $L_2\left(0,\infty \right)$ with Dirichlet boundary condition at $x=0.$