Let {s(j)}(infinity)(0) be a sequence of real numbers such that Hankel matrices S = s((i+j))(0)(infinity), S-(1) = (s(i+j+1))(0)(infinity) have finite numbers k, k(1) of negative eigenvalues. An indefinite moment problem with the moments s(j) (j = 0, 1,2,...) and the corresponding Stieltjes string are investigated. We use the approach via the Krein-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 a Krein space and a simple formula for the calculation of L-resolvent matric in terms of boundary operators are given. [References: 6]
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