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 Schr\"{o}dinger operator $H=-\partial {x}^{2}+q\left( x\right) $ on $L{2}\left( 0,\infty \right) $ with Dirichlet boundary condition at $x=0.$