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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

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