Abstract
AbstractLet (sj)∞j=0 be a sequence of real numbers such that the Hankel matrices (si+j)∞0, (Si+j+i)∞0 have finite numbers of negative eigenvalues. The indefinite moment problem with the moments Sj (j = 0,1,2, …) and the corresponding Stieltjes string are investigated. We use the approach via the Kreîn — Langer extension theory of symmetric operators in spaces with indefinite metric. In the framework of this approach a description of L– resolvents of a class of symmetric operators in Kreîn space and a simple formula for the calculation of the L– resolvent matrix in terms of boundary operators are given.
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