|
|
| |
| Eventual Positivity of Hermitian Polynomials and Integral Operators |
| |
Citation： |
Colin TAN.Eventual Positivity of Hermitian Polynomials and Integral Operators[J].Chinese Annals of Mathematics B,2016,37(1):83~94 |
| Page view： 3479
Net amount： 1374 |
Authors： |
Colin TAN; |
|
|
| Abstract： |
Quillen proved that if a Hermitian bihomogeneous polynomial is
strictly positive on the unit sphere,
then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares.
Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from
the eventual positive-definiteness of an associated integral operator. Their
arguments involve asymptotic expansions of the Bergman kernel. The
goal of this article is to give an elementary proof of the
positive-definiteness of this integral operator. |
Keywords： |
Asymptotics, Polynomial, Positivity |
Classification： |
13F20, 34E05 |
|
|
Download PDF Full-Text
|
|
|
|
