Subharmonicity of Powers of Octonion-Valued Monogenic Functions and Some Applications
Alexander Kheyfits, David Tepper, Bull. Belg. ath. Soc. 13 (2006), 609–617
(Received by the editors May 2005. Communicated by F. Brackx.)
It is proven that for an octonion-valued monogenic function f(x), x ∈ R^8,
its powers |f|^p are subharmonic for any p ≥ 6/7. This implies, in particular,
Hadamard’s three circles and three lines theorems and a Phragmen-Lindeloef
theorem for monogenic functions.
Key words and phrases : Octonion-valued monogenic functions; Subharmonicity of powers.
2000 Mathematics Subject Classification : 30G35; 31B05; 35E99.