On the Nevanlinna's Theory for Vector-Valued Mappings

Abstract EN

The purpose of this paper is to establish the first and second fundamental theorems for an E-valued meromorphic mapping from a generic domain D⊂ℂ to an infinite dimensional complex Banach space E with a Schauder basis.

It is a continuation of the work of C.

Hu and Q.

Hu.

For f(z) defined in the disk, we will prove Chuang's inequality, which is to compare the relationship between T(r,f) and T(r,f′).

Consequently, we obtain that the order and the lower order of f(z) and its derivative f′(z) are the same.