Generalized Dirichlet to Neumann map for moving initial-boundary value problems

We present an algorithm for characterizing the generalized Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectralanalysis of an associated ordinary differantial equation and on the use of the d-bar formalism. As an illustration, the Neumann boundary value for the linearized Schrödinger equation is determined in terms of the Dirichlet boundary value and of the initial condition.