On properties of matrix I(-1) of Sinc methods

In this paper, we study the determinant and eigen properties of $I^{(-1)},$ an important Toeplitz matrix used in Sinc methods. Some Sinc method applications depend on the non-singularity of this matrix and on the location of its eigenvalues. Among the theorems we prove is that $I^{(-1)}$ is nonsingular. We also show that if $\lambda $ is a pure imaginary eigenvalue of $I^{(-1)}$, then $|\lambda| > \frac{1}{\pi }$.