## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Subharmonicity of Powers of Octonion-Valued Monogenic Functions and Some Applications

#### Abstract

It is proven that for an octonion-valued monogenic function $f(\mathbf{x})$, $\mathbf{x} \in \mathbf{R}^8$, its powers $|f|^p$ are subharmonic for any $p\geq 6/7$. This implies, in particular, Hadamard's three circles and three lines theorems and a Phragmén-Lindelöf theorem for monogenic functions.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 4 (2006), 609-617.

Dates
First available in Project Euclid: 16 January 2007

https://projecteuclid.org/euclid.bbms/1168957338

Digital Object Identifier
doi:10.36045/bbms/1168957338

Mathematical Reviews number (MathSciNet)
MR2300618

Zentralblatt MATH identifier
1154.30037

#### Citation

Kheyfits , Alexander; Tepper, David. Subharmonicity of Powers of Octonion-Valued Monogenic Functions and Some Applications. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 4, 609--617. doi:10.36045/bbms/1168957338. https://projecteuclid.org/euclid.bbms/1168957338