Publication: Positive semidefinite germs in real analytic surfaces.
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Publication Date
2002
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Springer
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Abstract
We find all real analytic surface germs in R3 on which every positive semidefinite function germ is a sum of squares (in fact, of two squares) of analytic function germs.
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C. Andradas, L. Br¨ocker, J.M. Ruiz: Constructible sets in real geometry. Ergeb. Math.33. Berlin Heidelberg NewYork: Springer Verlag, 1996
M. Artin: On the solution of analytic equations, Invent. Math. 5, 227–291 (1968)
J. Bochnak, M. Coste, M.F. Roy: Real Algebraic Geometry, Ergeb. Math. 36 Berlin Heidelberg NewYork: Springer-Verlag, 1998
A. Chenciner: Courbes algebriques planes, Publ. Math. Univ. Paris VII, 1979
M.D. Choi, Z.D. Dai, T.Y.Lam, B. Reznick: The Pythagoras number of some affine algebras and local algebras, J. reine Angew. Math. 336, 45-82 (1982)
M.D. Choi, T.Y.Lam, B. Reznick, A. Rosenberg: Sums of squares in some integral domains, J. Algebra 65, 234–256 (1980)
J.F. Fernando, J.M. Ruiz: Positive semidefinite germs on the cone, Pacific. J. Math. (to appear)
H. Kurke, T. Mostowski, G. Pfister, D. Popescu, M. Roczen: Die Approximationseigenschaft lokaler Ringe, Lecture Notes in Math. 634. Berlin: Springer-Verlag, 1978
J.M. Ruiz: A note on a separation problem, Arch. Math. 43, 422–426 (1984)
J.M. Ruiz: On Hilbert’s 17th problem and real nullstellensatz for global analytic functions, Math. Z. 190, 447–459 (1985)
J.M. Ruiz: Sums of two squares in analytic rings, Math. Z. 230, 317–328 (1999)
C. Scheiderer: Sums of squares of regular functions on real algebraic varieties, Trans. A.M.S. 352(3),1039–1069 (1999)
C. Scheiderer: On sums of squares in local rings, Preprint Univ. Duisburg 2000