Problems and progress in multidimensional systems theory

The paper presents the troubles and trends of research in multidimensional system theory, with special emphasis in the areas of multivariable network analysis and synthesis, and multidimensional digital filters. The possibilities as well as perils of extending established single-dimensional techniques to multidimensional situations is discussed, and the nature and effect of certain fundamental problems present when applying the mathematics of several variables is given cognizance. Open problems are identified at various stages and some recommendations for future research are made.