Interpolation and local data for meromorphic matrix and operator functions

The main result of this paper is a generalization of the Mittag-Leffler theorem to matrix and operator valued meromorphic functions. Namely, a meromorphic matrix or operator valued function is constructed when the singular parts of the function and if its inverse are given in all singular points (which are assumed to be isolated). The paper contains also interpolation theorems based on other forms of local data (Jordan chains from left and right of the function and its inverse). An analysis of the local data, which is used in the proofs of these theorems is also included.Dedicated to the memory of D.P. MilmanThe research of this author partially supported by the Fund for Basic Research administrated by the Israel Academy of Science and Humanities.