A uniqueness theorem for meromorphic functions

In this paper, we prove the uniqueness theorem for a special class of meromorphic functions on the complex plane C. In particular, we study the class of meromorphic functions f in the domain C K', where $K'$ is the finite set of limit points of simple poles of the function f. In this class, we describe non-trivial subclasses in which every function f can be uniquely determined by the residues of the function f at its poles. The result covered in this paper is a part of a problem in a spectral operator theory.