I have a semi infinite toeplitz matrix of the form
$
A=\left(\begin{array}{ccccc}
A_{0} & A_{1} & 0 & 0 & \cdots\\
A_{-1} & A_{0} & A_{1} & 0 & \cdots\\
0 & A_{-1} & A_{0} & A_{1} & \cdots\\
0 & 0 & A_{-1} & A_{0} & \cdots\\
\vdots & \vdots & \vdots & \vdots & \ddots
\end{array}\right)
$,
where $A_0$, $A_1$ and $A_{-1}$ are finite n by n matrices. Is it possible to obtain the upper left n by n block of the inverse $A^{-1}$ of $A$ ? And is there maybe even a general solution for $A^{-1}$ ?
Best and thanks, Marius