complex Hessian matrix
Then the is the matrix
When applied to tangent vectors of the zero set of ,
it is called the Levi form and used to define a Levi
pseudoconvex point of a boundary of a domain. Note that the
matrix is not the same as the (real) Hessian. A twice continuously
differentiable real valued
function with a
positive semidefinite real Hessian matrix at every point is convex, but a function with
positive semidefinite matrix at every point is
plurisubharmonic (since it’s
continuous
it’s also called a pseudoconvex function).
References
- 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title | complex Hessian matrix |
---|---|
Canonical name | ComplexHessianMatrix |
Date of creation | 2013-03-22 14:31:16 |
Last modified on | 2013-03-22 14:31:16 |
Owner | jirka (4157) |
Last modified by | jirka (4157) |
Numerical id | 7 |
Author | jirka (4157) |
Entry type | Definition |
Classification | msc 32-00 |
Related topic | HessianMatrix |