Abstract.
Consider a Borel probability measure μ on the real line, and denote by {μ t : t≥1} the free additive convolution semigroup defined by Nica and Speicher. We show that the singular part of μ t is purely atomic and the density of μ t is locally analytic, provided that t > 1. The main ingredient is a global inversion theorem for analytic functions on a half plane.
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Mathematics Subject Classification (2000): 46L54, 30A99
Supported in part by a grant from the National Science Foundation.
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Belinschi, S., Bercovici, H. Atoms and regularity for measures in a partially defined free convolution semigroup. Math. Z. 248, 665–674 (2004). https://doi.org/10.1007/s00209-004-0671-y
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DOI: https://doi.org/10.1007/s00209-004-0671-y