Entries of continuous functions of large Hermitian tridiagonal 2-Toeplitz matrices

In this paper we present an eigenvalue decomposition for any real symmetric tridiagonal 2-Toeplitz matrix of odd order, where the eigenvector matrix is orthogonal. Using this decomposition we study the entries of continuous functions of large real symmetric tridiagonal 2-Toeplitz matrices. Furthermore, we also study in the present paper the entries of continuous functions of large Hermitian Toeplitz matrices with at most three non-zero diagonals.