INDEFINITE MOMENT PROBLEM AND RESOLVENT MATRICES OF HERMITIAN OPERATORS IN KREIN SPACES

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) h ave finite numbers k, k(1) of negative eigenvalues. An indefinite mome nt problem with the moments s(j) (j = 0, 1,2,...) and the correspondin g Stieltjes string are investigated. We use the approach via the Krein -Langer extension theory of symmetric operators in spaces with indefin ite metric. In the framework of this approach a description of L-resol vents 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.