Some applications of Schmüdgen's representation theorem

Thời gian: 15:00 đến 16:30 Ngày 27/03/2019

Địa điểm: C2-714, VIASM

Báo cáo viên: Lê Công Trình

Tóm tắt:

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.