Let H N = (s n+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 λ N of H N . It is proved that λ N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of λ N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where λ N is known to be bounded below, we prove that the limit of the n'th smallest eigenvalue of H N for N → ∞ tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed.

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Let X be a homogeneous tree of degree q + 1 (2 ≤ q ≤ ∞) and let ψ : X × X → C be a function for which ψ(x, y) only depend on the distance between x, y ∈ X. Our main result gives a necessary and sufficient condition for such a function to be a Schur multiplier on X ×X. Moreover, we find a closed expression for the Schur norm ψ S of ψ. As applications, we obtain a closed expression for the completely bounded Fourier multiplier norm · M 0 A(G) of the radial functions on the free (non-abelian) group F N on N generators (2 ≤ N ≤ ∞) and of the spherical functions on the p-adic group P GL 2 (Q q ) for every prime number q.