J-UNITARY PRESERVING AUTOMORPHISMS OF RATIONAL MATRIX FUNCTIONS - STATE-SPACE THEORY, INTERPOLATION, AND FACTORIZATION

Let GL(m)(R) be the multiplicative group of C(mXm) valued rational fun ctions of one complex variable z with determinant not vanishing identi cally. We analyze general inner automorphisms of GL(m)(R) that preserv e the set of matrix functions whose values are unitary with respect to an indefinite scalar product) for real, or unimodular, values of z. T he analysis is based on state space representations. In particular, ho mogeneous interpolation problems are studied for the rational matrix f unctions associated with such a general inner automorphism. We also de velop results on minimal factorizations within the group associated wi th a J-unitary preserving generalized inner automorphism.