Sample maximum and minimum

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In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space of the form

where is a bounded connected open subset of and are holomorphic on D.[1] If above are polynomials, then the set is called a polynomial polyhedron. Every analytic polyhedron is a domain of holomorphy (thus, pseudo-convex.)

The boundary of an analytic polyhedron is the union of the set of hypersurfaces

An analytic polyhedron is a Weil polyhedron, or Weil domain if the intersection of hypersurfaces has dimension no greater than .[2]

See also: the Behnke–Stein theorem.

References

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  • Lars Hörmander. An Introduction to Complex Analysis in Several Variables, North-Holland Publishing Company, New York, New York, 1973.

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  1. http://www.emis.de/journals/UIAM/PDF/45-139-145.pdf
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