Some applications of Schmüdgen's representation theorem

Time: 15:00 to  16:30 Ngày 27/03/2019

Venue/Location: C2-714, VIASM

Speaker: Lê Công Trình


In this talk I introduce a version of  Schmüdgen's representation theorem for the algebra of polynomial matrices and give some applications of this theorem. Firstly, we give a representation for polynomial matrices  positive definite on subsets of compact polyhedra. Then we establish a Putinar-Vasilescu Positivstellensatz for homogeneous and non-homogeneous polynomial matrices. Finally, we propose a matrix version of the Pólya -Putinar-Vasilescu Positivstellensatz.