Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 805-839

LOG-BIHARMONICITY AND A JENSEN FORMULA IN THE SPACE OF QUATERNIONS

Amedeo Altavilla and Cinzia Bisi

Università di Roma Tor Vergata, Dipartimento Di Matematica
Via Della Ricerca Scientifica 1, 00133, Roma, Italy; altavilla 'at' mat.uniroma2.it

Università di Ferrara, Dipartimento di Matematica e Informatica
via Machiavelli 35, I-44121 Ferrara, Italy; bsicnz 'at' unife.it

Abstract. Given a complex meromorphic function, it is well defined its Riesz measure in terms of the laplacian of the logarithm of its modulus. Moreover, related to this tool, it is possible to prove the celebrated Jensen formula. In the present paper, using among the other things the fundamental solution for the bilaplacian, we introduce a possible generalization of these two concepts in the space of quaternions, obtaining new interesting Riesz measures and global (i.e. four dimensional), Jensen formulas.

2010 Mathematics Subject Classification: Primary 30G35; Secondary 32A30, 31A30.

Key words: Slice regular functions, bi-harmonic functions, Jensen's formula, Riesz measure.

Reference to this article: A. Altavilla and C. Bisi: Log-biharmonicity and a Jensen formula in the space of quaternions. Ann. Acad. Sci. Fenn. Math. 44 (2019), 805-839.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4447