Publication: Positive semidefinite germs on the cone
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2002
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Pacific Journal of Mathematics
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Abstract
We show that any positive semidefinite analytic function germ on the cone z(2) = x(2) + y(2) is a sum of two squares of analytic function germs.
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C. Andradas, L. Br¨ocker and J.M. Ruiz, Constructible Sets in Real Geometry,Ergeb. Math., 33, Springer Verlag, Berlin-Heidelberg-New York, 1996,MR 98e:14056, Zbl 0873.14044.
S.Basarab, V. Nica and D. Popescu,Approximation properties and existencial completeness for ring morphisms, Manuscripta Math., 33 (1981), 227-282,MR 82k:03047, Zbl 0472.13013.
M.D. Choi, Z.D. Dai, T.Y. Lam and B. Reznick, The Pythagoras number of some affine algebras and local algebras, J. Reine Angew. Math., 336 (1982),45-82, MR 84f:12012, Zbl 0523.14020.
P. Jaworski, About estimates on mumber of squares necessary to represent a positive-semidefinite analytic function, Arch. Math., 58 (1992), 276-279,MR 93c:32008, Zbl 0748.14021.
J.Ortega, On the Pythagoras number of a realirreducible algebroid curve, Math.Ann., 289 (1991), 111-123, MR 92a:14065, Zbl 0743.14041.
G. P´olya and G. Szeg¨o, Problems and Theorems in Analysis I & II,Springer Study Edition, Springer Verlag, New York-Heidelberg-Berlin, 1976,MR 49 #8782, MR 53 #2.
R. Quarez, Pythagoras numbers of real algebroid curves and Gram matrices, J.Algebra, 238(1) (2001), 139-158.
J.M. Ruiz, The Basic Theory of Power Series, Advanced Lectures in Mathematics,Vieweg Verlag, Braunschweig Wiesbaden, 1993, MR 94i:13012.
Sums of two squares in analytic rings, Math. Z., 230 (1999), 317-328,Zbl 0930.32007.
R.J. Walker, Algebraic Curves, Springer Verlag, Berlin-Heidelberg-New York,