2005/06/06 by Vadim M Adamyan, Adamyan, Vadim M, Jose L Iserte +3
Mathematics · #15A60 (Primary) #47B35 #82D75 (Secondary) #92C55 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:15A60 #msc:47B35 #msc:82D75 #msc:92C55
paper · pdf · doi:10.48550/arxiv.math/0506091
20 pages, 8 figures
arxiv created 2005/06/06 · arxiv updated 2009/12/01
Asymptotic forms of the Hilbert-Scmidt and Hilbert norms of positive definite Toeplitz matrices QN=(b(j-k))j,k=0N-1 as N→ ∞ are determined. Here b(j) are consequent trigonometric moments of a generating non-negative mesure dσ(θ) on [ -π,π] . It is proven that σ(θ) is continuous if and only if any of those contributions is o(N). Analogous criteria are given for positive integral operators with difference kernels. Obtained results are applied to processing of stationary random signals, in particular, neutron signals emitted by boiling water nuclear reactors.