Riv. Mat. Univ. Parma, Vol. 11, No. 1, 2020
Alessandro Perotti [a]
A four dimensional Jensen formula
Pages: 139-152
Received: 30 November 2018
Accepted in revised form: 18 February 2019
Mathematics Subject Classification (2010): 30G35, 31A30.
Keywords: Jensen formula, slice-regular functions.
Authors address:
[a]: Department of Mathematics, University of Trento, Via Sommarive 14, Trento, I-38123, Italy
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Abstract:
We prove a Jensen formula for slice-regular functions of one quaternionic variable.
The formula relates the value of the function and of its first two derivatives at a point
with its integral mean on a three dimensional sphere centred at that point and with the disposition of its zeros.
The formula can be extended to semiregular slice functions.
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