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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.
Sushchyk et al. (Wed,) studied this question.
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