ON INDEFINITE MOMENT PROBLEMS AND RESOLVENT MATRICES OF HERMITIAN OPERATORS IN KREIN SPACES

Let (s(j))(j=0)(infinity) be a sequence of real numbers such that the Hankel matrices (s(i+j))(0)(infinity), (s(i+j+1))(0)(infinity) have fi nite numbers of negative eigenvalues. The indefinite moment problem wi th the moments s(j) (j = 0, 1, 2,...) and the corresponding Stieltjes string are investigated. We use the approach via the Krein-Langer exte nsion theory of symmetric operators in spaces with indefinite metric. In the framework of this approach a description of L-resolvents of a c lass of symmetric operators in Krein space and a simple formula for th e calculation of the L-resolvent matrix in terms of boundary operators are given.