Bondar A. Submanifolds of compact operators with fixed structure of Jordan blocks

The main results of the dissertation are following: two parameterizations of compact operator's submanifolds, with fixed structure of Jordan blocks are defined: obtained the codimantion formula and the type of operators that forms the tangent space); the sufficient conditions for the existence of a smooth structure in the family of elliptic differential operators on compact areas with fixed Jordan form are formulated; all one-parameter families of matrices, which keep the Jordan structure are described; the perturbations that extreme change the Jordan structures are founded (transformation to the diagonal matrix and to the single Jordan block).