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Log-biharmonicity and a Jensen formula in the space of quaternions. (English) Zbl 1422.30072

Summary: 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.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
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