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.
Publié le : 2007-07-14
Classification:
Potential theory on a Cartier tree,
subordinate structure,
polypotentials,
31C20,
31D05
@article{1187916321,
author = {Anandam, Victor and Bajunaid, Ibtesam},
title = {On non-commutative extensions of $\widehat{\G}\_a$ by $\widehat{\Gg}^{(M)}$\\ over an ${\F}\_p$-algebra},
journal = {Hiroshima Math. J.},
volume = {37},
number = {1},
year = {2007},
pages = { 277-314},
language = {en},
url = {http://dml.mathdoc.fr/item/1187916321}
}
Anandam, Victor; Bajunaid, Ibtesam. On non-commutative extensions of $\widehat{\G}_a$ by $\widehat{\Gg}^{(M)}$\\ over an ${\F}_p$-algebra. Hiroshima Math. J., Tome 37 (2007) no. 1, pp. 277-314. http://gdmltest.u-ga.fr/item/1187916321/