  Truncated moment problems in the class of generalized Nevanlinna functions
are investigated. General solvability criteria will be established, covering
both the even and odd problems, including complete parametrizations of
solutions. The main new results concern the case where the corresponding Hankel
matrix of moments is degenerate. One of the new effects which reveals in the
indefinite case is that the degenerated moment problem may have infinitely many
solutions. However, with a careful application of an indefinite analogue of a
step-by-step Schur algorithm a complete description of the set of solutions
will be obtained.

Functional Analysis