A NOTE ON POSITIVSTELLENSATZE FOR ̈ MATRIX POLYNOMIALS

Thi Hoa Bınh Du

Abstract


Abstract

In this paper we give a note on the relation of the positivity of polynomial matrices and their homogenizations on basic closed semi-algebraic sets. Base on this relation, we extend Putinar-Vasilescu’s Positivstel lensatz, in particular, Reznick’s Positivstellensatz, and Dickinson-Povh’s Positivstellensatz to (not necessarily homogeneous) polynomial matrices. This is a continuation of the work [C.-T. Lˆe, Some Positivstellens ̈atze for polynomial matrices, Positivity 19 (3) (2015), 513-528].


Refbacks

  • There are currently no refbacks.