Transfer functions models of linear systems are a well established tool for the design and analysis of one-dimensional systems. This is not the case for multidimensional physical systems, given in terms of initial boundary value problems. Here, the only mathematical description of widespread use are partial differential equations. This contribution shows, how the one-dimensional transfer function concept can be generalized to multidimensional systems with initial and boundary conditions. The idea is first introduced by a simple example and then extended to arbitrary spatial dimensions, general boundary conditions, space dependent coefficients and non self-adjoint differential operators.
Rabenstein, R. (1998). Transfer function models of multidimensional physical systems. (pp. 1/1-1/7). London, GB: Institute of Electrical Engineers.
Rabenstein, Rudolf. "Transfer function models of multidimensional physical systems." Proceedings of the Digest of the IEE Coll. on Multidimensional Systems, London Institute of Electrical Engineers, 1998. 1/1-1/7.