N. I. Akhiezer, The Classical Moment Problem, 1965.

C. Berg, J. P. Christensen, and P. , Positive definite functions on Abelian semigroups, Mathematische Annalen, vol.39, issue.3, pp.253-272, 1976.
DOI : 10.1007/BF01360957

URL : http://www.digizeitschriften.de/download/PPN235181684_0223/PPN235181684_0223___log43.pdf

C. Berg and P. H. Maserick, Exponentially bounded positive definite functions, Illinois Journal of Mathematics, vol.28, pp.162-179, 1984.

R. E. Curto and L. A. Fialkow, Solution of the truncated complex moment problem for flat data. Memoirs of the, Amer. Math. Soc, vol.119, 1996.

R. E. Curto and L. A. Fialkow, Flat extensions of positive moment matrices: recursively generated relations, Memoirs of the American Mathematical Society, vol.136, issue.648, 1998.
DOI : 10.1090/memo/0648

R. E. Curto and L. A. Fialkow, The truncated complex K-moment problem, Trans. Amer. Math. Soc, vol.352, p.28252855, 2000.

B. Fuglede, The multidimensional moment problem, Expositiones Mathematicae, vol.1, pp.47-65, 1983.

D. Henrion and J. B. Lasserre, Detecting Global Optimality and Extracting Solutions in GloptiPoly, Positive Polynomials in Lecture Notes on Control and Information Sciences, pp.293-310, 2005.
DOI : 10.1007/10997703_15

A. Kehrein, M. Kreuzer, and L. Robbiano, An algebraist???s view on border bases, Solving Polynomial Equations -Foundations, Algorithms and Applications, pp.169-202, 2005.
DOI : 10.1007/3-540-27357-3_4

J. B. Lasserre, M. Laurent, B. Mourrain, P. Rostalski, and P. Trebuchet, Moment matrices, border bases and real radical ideals, 2009.

J. B. Lasserre, Global Optimization with Polynomials and the Problem of Moments, SIAM Journal on Optimization, vol.11, issue.3, pp.796-817, 2001.
DOI : 10.1137/S1052623400366802

J. B. Lasserre, M. Laurent, and P. Rostalski, Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals, Foundations of Computational Mathematics, vol.16, issue.1, pp.607-647, 2008.
DOI : 10.1007/s10208-007-9004-y

J. B. Lasserre, M. Laurent, and P. Rostalski, A prolongation???projection algorithm for computing the finite real variety of an ideal, Theoretical Computer Science, vol.410, issue.27-29, 2008.
DOI : 10.1016/j.tcs.2009.03.024

M. Laurent, Revisiting two theorems of Curto and Fialkow on moment matrices, Proceedings of the American Mathematical Society, vol.133, issue.10, pp.2965-2976, 2005.
DOI : 10.1090/S0002-9939-05-08133-5

M. Laurent, Sums of Squares, Moment Matrices and Optimization Over Polynomials, Emerging Applications of Algebraic Geometry of IMA Volumes in Mathematics and its Applications, pp.157-270, 2009.
DOI : 10.1007/978-0-387-09686-5_7

B. Mourrain, A New Criterion for Normal Form Algorithms, Proceedings of the 13th International Symposium on Applied Algebra, pp.430-443, 1999.
DOI : 10.1007/3-540-46796-3_41

B. Mourrain and V. Y. Pan, Multivariate Polynomials, Duality, and Structured Matrices, Journal of Complexity, vol.16, issue.1, pp.110-180, 2000.
DOI : 10.1006/jcom.1999.0530

URL : https://hal.archives-ouvertes.fr/inria-00073171

M. Schweighofer, A Gröbner basis proof of the flat extension theorem for moment matrices, 2008.

J. Stochel, Solving the truncated moment problem solves the full moment problem, Glasgow Mathematical Journal, vol.43, issue.03, pp.335-341, 2001.
DOI : 10.1017/S0017089501030130

L. Vandenberghe and S. Boyd, Semidefinite Programming, SIAM Review, vol.38, issue.1, pp.49-95, 1996.
DOI : 10.1137/1038003

M. Laurent, C. Wiskunde, and &. Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands E-mail address