This is a request for support for a research conference to be held in June of 1987 in Phoenix, Arizona. The emphasis of the conference will be on operator theory and functional analysis. In particular, speakers will describe their latest contributions to operator theory, systems, the functional analysis side of complex variables (both in one and several variables), and operator algebras. The conference is designed to mesh with a mathematical engineering conference to be held immediately following. Several of the speakers at the engineering conference will be invited to give expository talks at this meeting on mathematical problems and methods in engineering. This meshing of the meetings should increase the scientific interaction between mathematicians and scholars in theoretical engineering.