Shift invariant manifolds and nonlinear analytic function theory

Abstract

The ultimate goal of our campaign is to generalize a substantial collection of results in classical complex variables to highly nonlinear situations. In [BH1] and subsequent works (c. f. [BGR],[H]) it was shown how an extension of the classical Beurling-Lax-Halmos theorem to Hilbert spasces with a signed bilinear form (indefinite metric) could be regarded as the key to many theorems in complex analysis. Thus our approach to the nonlinear case is to first extend our indefinite metric Beurling-Lax-Halmos theory to nonlinear situations that is the subject of this article.