On the Stieltjes moment problem on semigroups
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N. I. Akhiezer: The Classical Moment Problem. Oliver and Boyd, Edinburgh, 1965.
C. Berg: Positive definite and related functions on semigroups. In: The Analytical and Topological Theory of Semigroups (K. H. Hofmann, J. D. Lawson and J. S. Pym, eds.). Walter de Gruyter & Co., Berlin, 1990.
C. Berg, J. P.R. Christensen and C.U. Jensen: A remark on the multidimensional moment problem. Math. Ann. 243 (1979), 163–169.
C. Berg, J. P. R. Christensen and P. Ressel: Harmonic Analysis on Semigroups. Springer-Verlag, Berlin, 1984.
T. M. Bisgaard: Extension of characters on *-semigroups. Math. Ann. 282 (1988), 251–258.
T. M. Bisgaard: Separation by characters or positive definite functions. Semigroup Forum 53 (1996), 317–320.
T. M. Bisgaard: Semigroups of moment functions. Ark. Mat. 35 (1997), 127–156.
T. M. Bisgaard: On perfect semigroups. Acta Math. Hung. 79 (1998), 269–294.
T. M. Bisgaard: Extensions of Hamburger's Theorem. Semigroup Forum 57 (1998), 397–429.
T. M. Bisgaard: A method of moments for semigroups S without zero, but satisfying S = S + S. Semigroup Forum 61 (2000), 317–332.
T. M. Bisgaard: Semiperfect countable C-finite semigroups satisfying S = S +S. Math. Ann. 315 (1999), 141–168.
T. M. Bisgaard and P. Ressel: Unique disintegration of arbitrary positive definite functions on *-divisible semigroups. Math. Z. 200 (1989), 511–525.
A. Brøndsted: An Introduction to Convex Polytopes. Springer-Verlag, Berlin, 1983.
A. H. Clifford and G. B. Preston: The Algebraic Theory of Semigroups. American Mathematical Society, Providence, 1961.
D. Hilbert: Ñber die Darstellung definiter Formen als Summe von Formenquadraten. Math. Ann. 32 (1888), 342–350.
W. B. Jones, O. Njåstad and W. J. Thron: Orthogonal Laurent polynomials and the strong Hamburger moment problem. J. Math. Anal. Appl. 98 (1984), 528–554.
S. L. Lauritzen: Extremal Families and Systems of Sufficient Statistics. Springer-Verlag, Berlin, 1988.
A.W. Marshall and I. Olkin: Inequalities: Theory of Majorization and its Applications. Academic Press, New York, 1979. 195
N. Sakakibara: Moment problems on subsemigroups of ℕk 0 and ℤk. Semigroup Forum 45 (1992), 241–248.
K. Schmüdgen: An example of a positive polynomial which is not a sum of squares of polynomials. A positive, but not strongly positive functional. Math. Nachr. 88 (1979), 385–390.
T. J. Stieltjes: Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse Math. 8 (1894), 1–122; 9 (1894), 1-47.