Hiroshima Mathematical Journal
- Hiroshima Math. J.
- Volume 37, Number 2 (2007), 277-314.
On non-commutative extensions of $\widehat{\G}_a$ by $\widehat{\Gg}^{(M)}$\\ over an ${\F}_p$-algebra
Victor Anandam and Ibtesam Bajunaid
Abstract
Potential theory on a Cartier tree $T$ is developed on the lines of the classical and the axiomatic theories on harmonic spaces. The harmonic classifications of such trees are considered; the notion of a subordinate structure on $T$ is introduced to consider more generally the potential theory on $T$ associated with the Schrödinger equation $\Delta u\left( x\right) =Q\left(x\right) u\left( x\right) ,Q\left( x\right) \geq 0$ on $T$; polysuperharmonic functions and polypotentials on $T$ are defined and a Riesz-Martin representation for positive polysuperharmonic functions is obtained.
Article information
Source
Hiroshima Math. J., Volume 37, Number 2 (2007), 277-314.
Dates
First available in Project Euclid: 24 August 2007
Permanent link to this document
https://projecteuclid.org/euclid.hmj/1187916321
Digital Object Identifier
doi:10.32917/hmj/1187916321
Mathematical Reviews number (MathSciNet)
MR2345370
Subjects
Primary: 31C20: Discrete potential theory and numerical methods 31D05: Axiomatic potential theory
Keywords
Potential theory on a Cartier tree subordinate structure polypotentials
Citation
Anandam, Victor; Bajunaid, Ibtesam. On non-commutative extensions of $\widehat{\G}_a$ by $\widehat{\Gg}^{(M)}$\\ over an ${\F}_p$-algebra. Hiroshima Math. J. 37 (2007), no. 2, 277--314. doi:10.32917/hmj/1187916321. https://projecteuclid.org/euclid.hmj/1187916321
