Eigenvalues of weighted generalized shifts over direct products of vector spaces

Abstract

In the following text for vector space $V$ over field $F$ we compute all eigenvalues of weighted generalized shift ${\sigma }_{\phi ,\mathfrak{w}}:V^{\Gamma }\to V^{\Gamma }$ (and generalized shift ${\sigma }_{\phi }:V^{\Gamma }\to V^{\Gamma }$) for nonempty set $\Gamma$, weight vector $\mathfrak{w}\in F^{\Gamma }$ and self--map $\phi :\Gamma \to \Gamma$.

8 pages