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math.OA2024
-valued semi-circular system and the free Poincaré inequality
Hyuga Ito
We characterize -valued semi-circular system in terms of -valued free probabilistic analogue of Poincaré inequality. This is a -valued generalization of Biane's theorem \c…
math.OA2023★ 2 cited
Differential calculus for fully matricial functions I
Hyuga Ito
We will introduce a cyclic derivative for fully (stably) matricial functions and study its basic properties. In particular, we will show the Poincaré lemma for stably matricial fun…