Positive harmonic functions on the Heisenberg group

author: Yves Benoist, National Center for Scientific Research (CNRS)
published: July 6, 2021,   recorded: July 2021,   views: 3

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A harmonic function on a group is a function which is equal to the average of its translates, average with respect to a finitely supported measure. First, we will survey the history of this notion. Then we will describe the extremal non-negative harmonic functions on the Heisenberg group. We will see that the classical partition function occurs as such a function and that this function is the only one beyond harmonic characters.

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