The Boundary Control Approach to the Titchmarsh-Weyl m–Function. I. The Response Operator and the A–Amplitude

Research paper by Sergei Avdonin, Victor Mikhaylov, Alexei Rybkin

Indexed on: 16 Aug '07Published on: 16 Aug '07Published in: Communications in Mathematical Physics

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 = −∂x2 + q(x) on L2(0, ∞) with Dirichlet boundary condition at x = 0.