Positivity conditions for Hermitian symmetric functions
| dc.creator | D'Angelo, John P. | |
| dc.creator | Varolin, Dror | |
| dc.date | 2003-06-13 | |
| dc.date.accessioned | 2026-07-07T04:58:57Z | |
| dc.date.available | 2026-07-07T04:58:57Z | |
| dc.description | We introduce a countable collection of positivity classes for Hermitian symmetric functions on a complex manifold, and establish their basic properties. We study a related notion of stability. The first main result shows that, if the underlying matrix of coefficients of an entire Hermitian symmetric function has at most k positive eigenvalues, then it can lie in the k-th positivity class only if it is a squared norm. We establish a similar result for Hermitian symmetric functions on the total space of a holomorphic line bundle. Finally we study the positivity classes for a natural one-parameter family of Hermitian metrics on a power of the universal bundle over complex projective space; we obtain sharp information about the parameter values in order to be in the k-th class. The paper closes with some additional information about the case when k is 2, where a nonlinear version of the Cauchy-Schwarz inequality arises. | |
| dc.description | Dedicated to Yum-Yong Siu on the occasion of his sixtieth birthday | |
| dc.identifier | https://arxiv.org/abs/math/0306220 | |
| dc.identifier | http://arxiv.org/abs/math/0306220 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67792 | |
| dc.subject | Complex Variables | |
| dc.title | Positivity conditions for Hermitian symmetric functions | |
| dc.type | text |