Some Phragmén-Lindelöf and harmonic majorization theorems for subharmonic functions
✍ Scribed by D.H Armitage; S.J Gardiner
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 868 KB
- Volume
- 102
- Category
- Article
- ISSN
- 0022-247X
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## 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: R
We consider the function f ( z ) analytic in the half plane Q+ = { z : Im z -0) and continuous in its closure. Theorems of the PHEAGMJ~N-LINDELOF type are characterized by assuming growth restrictions for If(z)l in the closure of @+, which are sufficient for i t to be bounded or at most of exponenti