Small eigenvalues of large Hankel matrices: The indeterminate case
نویسندگان
چکیده
In this paper we characterize the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we nd expressions for this lower bound in a number of indeterminate moment problems.
منابع مشابه
. C A ] 1 6 Ju l 1 99 9 Small eigenvalues of large Hankel matrices : The indeterminate case ∗
R xdα(x). (1.1) With α we associate the infinite Hankel matrix H∞ = {Hjk}, Hjk = sj+k. (1.2) LetHN be the (N+1)×(N+1) matrix whose entries areHjk, 0 ≤ j, k ≤ N . SinceHN is positive definite, then all its eigenvalues are positive. The large N asymptotics of the smallest eigenvalue, denoted as λN , of the Hankel matrix HN has been studied in papers by Szegö [11], Widom and Wilf [13], Chen and La...
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تاریخ انتشار 1999