Bergman–Weil formula
Encyclopedia
In mathematics, the Bergman–Weil formula is an integral representation for holomorphic function
s of several variables generalizing the Cauchy integral formula. It was introduced by and .
for functions fj that are holomorphic on some neighborhood of the closure of U, such that the faces of the Weil domain (where one of the functions is 1 and the others are less than 1) all have dimension 2n − 1, and the intersections of k faces have codimension
at least k.
Holomorphic function
In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain...
s of several variables generalizing the Cauchy integral formula. It was introduced by and .
Weil domains
A Weil domain is a domain U in Cn defined by inequalities fj(z) < 1for functions fj that are holomorphic on some neighborhood of the closure of U, such that the faces of the Weil domain (where one of the functions is 1 and the others are less than 1) all have dimension 2n − 1, and the intersections of k faces have codimension
Codimension
In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, and also to submanifolds in manifolds, and suitable subsets of algebraic varieties.The dual concept is relative dimension.-Definition:...
at least k.