1. Subharmonic functions on Carnot groups
- Author
-
Andrea Bonfiglioli and Ermanno Lanconelli
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,Subharmonic ,Subharmonic function ,Mathematics::Complex Variables ,General Mathematics ,Carnot group ,Mathematics::Spectral Theory ,Potential theory ,symbols.namesake ,Calculus ,symbols ,Mathematics::Metric Geometry ,Carnot cycle ,Representation (mathematics) ,Mathematics - Abstract
Many results of classical Potential Theory are extended to sub-Laplacians ▵𝔾 on Carnot groups 𝔾. Some characterizations of ▵𝔾-subharmonicity, representation formulas of Poisson-Jensen's kind and Nevanlinna-type theorems are proved. We also characterize the Riesz-measure related to bounded-above ▵𝔾-subharmonic functions in ℝ N .
- Published
- 2003