APS
Speaker: Debapriya Ojha, IIT Bombay
Host: Manoj Kumar Keshari
Title: Positive Polynomials on a Strip
Time, day and date: 12:00:00 PM – 1:00:00 PM, Friday, September 18
Venue: Room 113 (https://meet.google.com/vid-bpnc-ujc)
Abstract: Let F be a subfield of the real numbers R. Let S = {g1, . . ., gs} ⊂ F[x1, . . . , xn] be a finite set of polynomials in n variables and let K_S be the basic closed semialgebraic set generated by the non-negativity of S in R^n. Also, let U ⊂ F[t] be the natural choice of generators of a noncompact basic closed semialgebraic set K_U in R with boundary ∂K_U ⊂ F. We show that f ∈ F[x1, . . . , xn, t] > 0 on K_S × K_U and fully m-ic on K_S implies f belongs to the preordering of F[x1, . . . , xn, t] generated by S, U and non-negative elements of F.