This project is aimed at constructing a theory of contraction operators on Krein spaces which, in areas such as dilation and extension properties, parallels the Hilbert space case. Recent work has shown that dilations and extensions exist and can be characterized. New problems of labeling will be investigated. Examples include substitution operators induced by normalized Riemann mappings for subregions of the unit disk. A long-range goal is to apply the theory to a coefficient interpolation problem for Riemann mappings. This project is in the general area of modern analysis and involves the study of spaces and the transformations or operators on these spaces. Probably one of the most studied and valuable spaces in physics, analysis, and geometry is the Hilbert space. The Krein space examined in this project is a space with a scalar product which is decomposable as the orthogonal direct sum of a Hilbert space and the anti-space of a Hilbert space.
