where D is a bounded connected open subset of Cn, are
holomorphic on D and P is assumed to be
relatively compact in D.[1] If above are polynomials, then the set is called a polynomial polyhedron. Every analytic polyhedron is a
domain of holomorphy and it is thus
pseudo-convex.
The boundary of an analytic polyhedron is contained in the union of the set of hypersurfaces
An analytic polyhedron is a Weil polyhedron, or
Weil domain if the intersection of any k of the above hypersurfaces has dimension no greater than 2n-k.[2]
Severi, Francesco (1958), Lezioni sulle funzioni analitiche di più variabili complesse – Tenute nel 1956–57 all'Istituto Nazionale di Alta Matematica in Roma (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp. XIV+255,
Zbl0094.28002. Notes from a course held by Francesco Severi at the
Istituto Nazionale di Alta Matematica (which at present bears his name), containing appendices of Enzo Martinelli, Giovanni Battista Rizza and
Mario Benedicty. An English translation of the title reads as:-"Lectures on analytic functions of several complex variables – Lectured in 1956–57 at the Istituto Nazionale di Alta Matematica in Rome".
where D is a bounded connected open subset of Cn, are
holomorphic on D and P is assumed to be
relatively compact in D.[1] If above are polynomials, then the set is called a polynomial polyhedron. Every analytic polyhedron is a
domain of holomorphy and it is thus
pseudo-convex.
The boundary of an analytic polyhedron is contained in the union of the set of hypersurfaces
An analytic polyhedron is a Weil polyhedron, or
Weil domain if the intersection of any k of the above hypersurfaces has dimension no greater than 2n-k.[2]
Severi, Francesco (1958), Lezioni sulle funzioni analitiche di più variabili complesse – Tenute nel 1956–57 all'Istituto Nazionale di Alta Matematica in Roma (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp. XIV+255,
Zbl0094.28002. Notes from a course held by Francesco Severi at the
Istituto Nazionale di Alta Matematica (which at present bears his name), containing appendices of Enzo Martinelli, Giovanni Battista Rizza and
Mario Benedicty. An English translation of the title reads as:-"Lectures on analytic functions of several complex variables – Lectured in 1956–57 at the Istituto Nazionale di Alta Matematica in Rome".