# Log-biharmonicity and a Jensen formula in the space of quaternions

```@article{Altavilla2017LogbiharmonicityAA,
title={Log-biharmonicity and a Jensen formula in the space of quaternions},
author={Amedeo Altavilla and Cinzia Bisi},
year={2017}
}```
• Published 16 August 2017
• Mathematics
• Annales Academiae Scientiarum Fennicae Mathematica
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…
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The continuity of ƒ at oo follows from the fact that \f(x)\ increases without limit as \x\ increases without limit, a fact which is obvious from the definition of/. It should be noted that this