Characteristic functions and Borel exceptional values of \(E\)-valued meromorphic functions (Q1938150)

Let \((E, \|\cdot\|)\) be an infinite dimensional complex Banach space with Schauder basis \(\{e_j\}\) and norm \( \|\cdot\|\). Any function \(f\) of \(z\in C_{R} = \{z: |z| < R\}\), \(0 < R \leq + \infty\), taking values in \(E\) can be written as \[ f(z) = \left(f_1(z), f_2(z), \dots, f_k(z), \dots\right). \] The class of \(E\)-valued functions is considered in this article. Such a function \(f\) is called holomorphic (meromorphic) in the disc \(C_{R}\) if all of its components are holomorphic (meromorphic). The paper presents some results of Nevanlinna-type for \(E\)-valued meromorphic functions, namely, the properties of the characteristic functions in the unit disc \(C_{1}\) are discussed and Borel exceptional values are characterized.