First Announcement

We are organizing a short meeting to be held in Pisa, March 12-13, 2004, on

Representation of semidefinite positive functions as sums of squares and related topics

For the polynomial rings this is known as "The Hilbert 17th problem". We want to focus on the same problem on more general spaces, in particular algebras of differentiable functions. Research on this topics was developed using both arguments from analysis in the phase space and from real and complex analytic geometry, and we want to underline these relations. Some survey talks are also scheduled to give the state of the art from several points of view.

Our best wishes for a merry Christmas and a happy new year.

F. Acquistapace, F. Broglia, F. Colombini

Tentative program

Friday, March 12.

9.15-10.15 A.Prestel: Sums of squares of polynomial functions. 10.30-11.30 J.-M.Bony: Nonnegative functions as sums of squares: the C^infinity and C^k case. 11.45-12.45 C.Andradas: Sums of squares of analytic functions.

15.00-16.00 P.W.Michor: To be annonced. 16.15-17.15 K.Schmuegden: To be confirmed. 17.45-18.45 L.Migliorini: Some analytic problems in Hodge's Theory of singular varieties.

Saturday, March 13

9.15-10.15 J.-M.Bony: The Fefferman-Phong inequality. 10.30-11.30 J.Fernando: Some advances about the 17 Hilbert problem for global analytic functions. 11.45-12.45 D.Del Santo: The Fefferman-Phong inequality in the locally tempered Weyl calculus.

15.00-15.45 F.Pieroni: Sums of squares in Quasi-analytic Denjoy-Carlemann classes. 16.00-16.45 L.Pernazza: Writing C^k functions as sums of squares of C^h functions: examples and counterexamples. 17.15-18.15 A.Parmeggiani:A natural inequality for systems: Sharp-Garding or Fefferman-Phong?

Interested people should send a message to one of the following addresses:

acquistf@dm.unipi.it broglia@dm.unipi.it colombini@dm.unipi.it