A strict positivstellensatz for global analytic functions
by
Francesca Acquistapace
Dip. di Matematica Universita' di Pisa
Coauthors: Carlos Andradas, Fabrizio Broglia

Let X be a global semianalytic basic closed set in the affine space. Let f be a global analytic function which is strictly positive on X. We prove that f may be written as

f = u0 +u1 f1+ ... +uk fk

where X = {f₁ >= 0, ..., f_k >= 0} and u₀, ..., u_k are squares. Note that we do not assume X to be compact and there is the module instead of the the cone, as in Schmudgen's result in the polynomial case. The proof is rather elementary.

Date received: June 25, 1999