Some Theorems of the PRAGMÉN‒LINDELÖF's Theory for Subharmonic Functions

✍ Scribed by M. Riedel

• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 313 KB
• Volume: 78
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19770780103

✦ Synopsis

Abstract

Some new results of the PRAGMÉN‒LINDELÖF theory in 𝔜~+~ (namely the elementary method of successive mapping [4] and ROSSBERG's [8] non‒elementary theorem) are carried over to subharmonic functions. The theorems have – in spite of their very different nature – a common salient feature: Restrictions on the rate of increase of the function under consideration are imposed not only in the whole of 𝔜~+~, but also on one or several rays in 𝔜~+~ starting from 0. Our method yields also a new proof of ROSSBERG's theorem [8] without any superfluous boundary conditions.