Factorization Theory for Stable, Discrete-Time Inner Functions
Paul A. Fuhrmann, Jörg Hoffmann · 1994
We develop a factorization theory for stable inner functions relative to the unit circle. paf/hoffmann/klhinner Earl Katz Family Chair in Algebraic System Theory y Partially supported by GIF under Grant No. I 184. 1 INTRODUCTION 2 1 Introduction Inner functions play an important role in both mathematics and its applications, particularly in the area of control and filtering theory. A classical result, proved by Beurling [1949] links inner functions with the theory of invariant subspaces. This provides another link with the theory of functional models for general, non selfadjoint operators. Our object in this paper is to describe a factorization theory for stable, matrix valued inner functions in state space terms. Characterizations of inner functions in the right half plane or in (outside) the unit circle have been known for a long time, e.g. Genin et al. [1983]. Factorizations of inner functions are related bijectively to the set of invariant subspaces of a model operator, that...