RT Journal Article T1 Positive semidefinite germs on the cone A1 Fernando Galván, José Francisco A1 Ruiz Sancho, Jesús María AB 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. PB Pacific Journal of Mathematics SN 0030-8730 YR 2002 FD 2002 LK https://hdl.handle.net/20.500.14352/57239 UL https://hdl.handle.net/20.500.14352/57239 LA eng NO 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, DS Docta Complutense RD 2 may 2024