Condition numbers of Hankel matrices for exponential weights (Q2577467)

The author investigates the rate of growth of \(\Lambda_n\) and \(\Lambda_n/ \lambda_n\), \(\Lambda_n(\lambda_n)\) the largest (the smallest) eigenvalue of the positive definite \(n\times n\) Hankel matrix \(H_n=[h^{(n)}_{j,k}]=[\int_{-d}^d t^{j+k}W^2(t)\,dt]\), \(0<d\leq \infty\), with a class of relatively general weights \(W^2=e^{-2Q}\) on \([-d,d]\), which is the even class of weights considered in the book by the author and \textit{E. Levin} [Orthogonal polynomials for exponential weights. (CMS Books in Mathematics 4, New York: Springer) (2001; Zbl 0997.42011)]. Special cases considered in more detail are \(Q(t)= |t|^\alpha\), \(\alpha>1\), \(t\in \mathbb{R}\), \(Q(t)=(1-t^2)^{-\alpha}-1\), \(\alpha>0\), \(0\leq t\leq 1\), and \(Q(t=(d^2-t^2)^{-\alpha}-d^{-2 \alpha}\), \(\alpha>0\), \(d>1\), \(-d\leq t\leq d\).