Journal article
Noncommutative plurisubharmonicity, existence of pluriharmonic conjugates, and free universal monodromy
Transactions of the American Mathematical Society
20 Feb 2026
Abstract
We fully characterize free noncommutative plurisubharmonic functions as compositions of a convex function with an analytic function, completing a long-standing program. The decomposition is essentially unique when the convex function is chosen to be of a natural form. The result is first established locally, and then Free Universal Monodromy implies the global result. Moreover, we see that plurisubharmonicity is a geometric property– a real analytic free function plurisubharmonic on a neighborhood is plurisubharmonic on the whole domain. We give an analytic Greene-Liouville theorem, an entire free plurisubharmonic function is a sum of hereditary and anti-hereditary squares. Our monodromic considerations imply that pluriharmonic free functions have globally defined pluriharmonic conjugates. We also describe why the Baker-Campbell-Hausdorff formula has finite radius of convergence in terms of monodromy, and, in doing so, solve a related problem of Martin-Shamovich.
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Details
- Title
- Noncommutative plurisubharmonicity, existence of pluriharmonic conjugates, and free universal monodromy
- Creators
- J. Pascoe - Drexel University
- Publication Details
- Transactions of the American Mathematical Society
- Publisher
- AMER MATHEMATICAL SOC
- Number of pages
- 20
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001697198700001
- Other Identifier
- 991022166476704721