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

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.Comment: Final Version. To appear on Annales Academiae Scientiarum Fennicae Mathematica, Volume 44 (2019