Riv. Mat. Univ. Parma, Vol. 11, No. 1, 2020

Alessandro Perotti [a]

A four dimensional Jensen formula

Pages: 139-152
Accepted in revised form: 18 February 2019
Mathematics Subject Classification (2010): 30G35, 31A30.
Keywords: Jensen formula, slice-regular functions.
[a]: Department of Mathematics, University of Trento, Via Sommarive 14, Trento, I-38123, Italy

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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