A uniqueness theorem for meromorphic functions

N. Sushchyk; D. Lukivska

doi:10.30970/ms.61.2.219-224

N. Sushchyk Ivan Franko National University of Lviv
D. Lukivska Ivan Franko National University of Lviv

DOI: https://doi.org/10.30970/ms.61.2.219-224

Keywords: meromorphic functions, Blaschke products

Abstract

In this paper, we prove the uniqueness theorem for a special class of meromorphic functions on the complex plane $\mathbb{C}$. In particular, we study the class of meromorphic functions $f$ in the domain $\mathbb{C}\setminus K'$, 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.

Author Biographies

N. Sushchyk, Ivan Franko National University of Lviv

Ivan Franko National University of Lviv

Lviv, Ukraine

D. Lukivska, Ivan Franko National University of Lviv

Ivan Franko National University of Lviv

Lviv, Ukraine

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