On the Nevanlinna classes of holomorphic functions on compact bordered Riemann surfaces
This paper contains the generalization of the theorem of F. and R. Nevanlinna for the case of the holomorphic functions on the compact bordered Riemann surface \(\Omega\), which belong to the Nevanlinna class N(\(\Omega\)). (f\(\in N(\Omega)\) if the subharmonic function \(\log^+| f|\) has a harmonic majorant.) The author proved: A holomorphic function f belongs to N(\(\Omega\)) iff it is the quotient of two functions being holomorphic in \(\Omega\). This theorem is used to the study of the boundary behaviour of holomorphic functions from the class N(\(\Omega\)).
scientific article; zbMATH DE number 4163231