Support of the Brown measure of the product of a free unitary Brownian motion by a free self-adjoint projection - Archive ouverte HAL Access content directly
Journal Articles Journal of Functional Analysis Year : 2022

Support of the Brown measure of the product of a free unitary Brownian motion by a free self-adjoint projection

Nizar Demni
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Tarek Hamdi
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Abstract

The first part of this paper is devoted to the Brown measure of the product of the free unitary Brownian motion by an arbitrary free non negative operator. Our approach follows the one recently initiated by Driver-Hall-Kemp though there are substantial differences at the analytical side. In particular, the corresponding Hamiltonian system is completely solvable and the characteristic curve describing the support of the Brown measure has a non-constant (in time) argument. In the second part, we specialize our findings to the product of the free unitary Brownian motion by a free self-adjoint projection and obtain an explicit description of its support.

Dates and versions

hal-03170485 , version 1 (16-03-2021)

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Nizar Demni, Tarek Hamdi. Support of the Brown measure of the product of a free unitary Brownian motion by a free self-adjoint projection. Journal of Functional Analysis, 2022, ⟨10.1016/j.jfa.2021.109362⟩. ⟨hal-03170485⟩
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