Year: 2008
Type: preprint
Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index $p$-harmonic function is a constant. For some normal subgroups of infinite index we describe a class of (non-constant) periodic $p$-harmonic functions. If $p\neq2$, the $p$-harmonicity is non-linear, i.e., the linear combination of $p$-harmonic functions need not be $p$-harmonic. In spite of this, we show that linear combinations of the $p$-harmonic functions described for normal subgroups of infinite index are also $p$-harmonic.
Source: arXiv (Cornell University)
Authors: Rozikov, U. A., Ishankulov, F. T.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394666819