Asymptotic Eigenvalue Expansions for Toeplitz Matrices with Certain Fisher–Hartwig Symbols

The present paper is a survey of some of the authors’ results on the asymptotic behavior of individual eigenvalues and eigenvectors of sequences of Toeplitz matrices when their size tends to infinity. The symbols of the matrices are supposed to have power singularities and are special cases of so-called Fisher–Hartwig symbols.