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arXiv · 0803.0804

On periodic $p$-harmonic functions on Cayley tree

U. A. Rozikov·F. T. Ishankulov
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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.

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U. A. Rozikov, F. T. Ishankulov. 2008-03-06. On periodic $p$-harmonic functions on Cayley tree. https://arxiv.org/abs/0803.0804

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