Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
ON HERMITIAN POLYNOMIAL OPTIMIZATION MIHAI PUTINAR
 

Summary: ON HERMITIAN POLYNOMIAL OPTIMIZATION
MIHAI PUTINAR
Abstract. We compare three levels of algebraic certificates for eval-
uating the maximum modulus of a complex analytic polynomial, on a
compact semi-algebraic set. They are obtained as translations of some
recently discovered inequalities in operator theory. Although they can
be stated in purely algebraic terms, the only known proofs for these
decompositions have a transcendental character.
1. Introduction
Let z = (z1, ..., zd) be the complex coordinates in Cd. Then real coordi-
nates of the underlying space R2d are denoted by x = (x1, ..., x2d), where
zk = xk +ixd+k. We will work in the polynomial algebra R[x], and consider
there the convex hulls:
2
= co{p2
; p R[x]},
and
2
h = co{|q|2
; q C[z]}.

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics