2009/06/24 by Christian Berg, Ryszard Szwarc · 1 citation
Computer Science · Mathematics · #Bounded function #Combinatorics #Eigenvalues and eigenvectors #Hankel matrix #Infinity #Lambda #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Measure (data warehouse) #Moment (physics) #Moment problem #Order (exchange) #Physics #Quantum mechanics #Spectral Theory in Mathematical Physics #Zero (linguistics) #math.CA #msc:15A18 #msc:42C05
paper · pdf · doi:10.1007/s00365-010-9109-4
published as Constr. Approx. 34 (2011), 107-133
arxiv created 2009/06/24 · openalex publication_date 2010/07/15 · arxiv updated 2017/01/31 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
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 lambdaN of HN. It is proved that lambdaN has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambdaN can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambdaN is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of HN for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed.