Proof of Stenger's conjecture on matrix I(−1) of Sinc methods

In this paper, we prove a conjecture, which was proposed by Frank Stenger in 1997, concerning the localization of eigenvalues of the Sinc matrix I(−1), a problem that is important in both the theory and the practice of Sinc methods. In 2003, Iyad Abu-Jeib and Thomas Shores established a partial answer to this unsolved problem. The techniques they have developed, however, turn out to be the key that finally leads to the settlement here of Stenger's conjecture.