Abstract:
In the space $l_\infty(\mathbb Z^3,\mathbb C)$, we consider the difference operator
\begin{equation*}
(\mathcal{A}x)_{n}=\sum_{k\in\mathbb{Z}^3}a_{k} x_{n-k},
\end{equation*}
which is invariant under the action of the group generated by rotations around the coordinate axes by the angle $\pi/2$. The equality of the coefficients $a_k$, $k\in\mathbb Z^3$, corresponding to the same orbit is established. A representation of the operator based on this property is proposed.
Keywords:difference operator, representation of a group, finite group, invariance, rotation group, orbit
Fulltext:
PDF file (274 kB)