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We prove that, if the sequences μη0, η = 0 , 1 , . . . , and μητη, η, τη = 0 , 1 , . . . give rise respectively to infinitely many solutions of the associated moment problems, then these solutions may be partially described by the formula f M J t z d ß ( t ) Β ( ζ ) φ ( ζ ) — D(z) The four functions A(z),B(z),C(z) and D(z) are certain limits of quasi-orthogonal functions and φ is in the extended Nevanlinna class. AMS 1991 subject classification: 30E05, 42C05

NEVANLINNA PARAMETRIZATION OF THE SOLUTIONS TO SOME RATIONAL MOMENT PROBLEMS