By the linearization property of Lipschitz-free spaces, any Lipschitz map $$f : M \rightarrow N$$ between two pointed metric spaces may be extended uniquely to a bounded linear operator $${\widehat{f}} {\mathcal {F}}(M) {F}}(N)$$ their corresponding spaces. In this note, we explore connections dynamics self-maps M$$ and extensions {F}}(M)$$ . This not only allows us relate topological dynamical...

Let $P$ be the isotropic nearest neighbor transition operator on a homogeneous tree. We consider $\lambda$-eigenfunctions of for $\lambda$ outside its $\ell^2$ spectrum, i.e., eigenfunctions with eigenvalue $\gamma=\lambda - 1$ Laplace $Delta=P- \mathbb I$, and also $\lambda-$polyharmonic functions, that is, union kernels $(Delta-\gamma I)^n$ $n\geqslant 0$. prove that, suitable Banach space ge...