Hankel matrices and the infinite companion

Infinite Hankel Block Matrices, Extremal Problems

In the paper we consider a matrix version of the extremal Nehary problem [1],[4]. Our approach is based on the notion of a matrix analogue of the eigenvalue ρ2min. The notion of ρ 2 min was used in a number of the extremal interpolation problems [2],[3],[7]. We note that ρ2min is a solution of a nonlinear matrix inequality of the Riccati type [2],[6], [7]. Our approach coincides with the Adamja...

Irreducible Toeplitz and Hankel matrices

An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.

Determinants of Hankel Matrices

The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval. The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.

Stable factorization for Hankel and Hankel-like matrices

The smallest eigenvalue of Hankel matrices

Let HN = (sn+m), n,m ≤ N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue λN of HN . It is proved that λN has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of λN can be arbitrarily slow or arbitrarily fast. In the indeterminate ca...