Title of article :
Small eigenvalues of large Hermitian moment matrices
Author/Authors :
Escribano، نويسنده , , C. and Gonzalo، نويسنده , , R. and Torrano، نويسنده , , E.، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2011
Abstract :
We consider an infinite Hermitian positive definite matrix M which is the moment matrix associated with a measure μ with infinite and compact support on the complex plane. We prove that if the polynomials are dense in L 2 ( μ ) then the smallest eigenvalue λ n of the truncated matrix M n of M of size ( n + 1 ) × ( n + 1 ) tends to zero when n tends to infinity. In the case of measures in the closed unit disk we obtain some related results.
Keywords :
Complex moment problem , orthogonal polynomials , Smallest eigenvalue , measures , Approximation by polynomials
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications