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In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space Cn of the form where D is a bounded connected open subset of Cn, are holomorphic on D and P is assumed to be relatively compact in D. 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

Attributes	Values
rdf:type	yago:WikicatSeveralComplexVariables yago:PhysicalEntity100001930 yago:Thing100002452 yago:Variable109468959
rdfs:label	Analytic polyhedron (en) Analytisk polyeder (sv)
rdfs:comment	Analytisk polyeder förekommer inom komplex analys (som är ett forskningsfält inom matematiken) och avser ett geometriskt objekt, ett speciellt slag av (öppet) område i ett flerdimensionellt komplext vektorrum, eller mer generellt i en komplex mångfald. Analytiska polyedrar är av intresse för sin speciella geometri och kanske mest för de analytiska egenskaper som objekt förknippade med dem därmed har. (sv) In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space Cn of the form where D is a bounded connected open subset of Cn, are holomorphic on D and P is assumed to be relatively compact in D. 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 (en)
dcterms:subject	Several complex variables
Wikipage page ID	21663267 (xsd:integer)
Wikipage revision ID	1059743376 (xsd:integer)
Link from a Wikipage to another Wikipage	Behnke–Stein theorem Pseudoconvex set Walter de Gruyter Belmont, California Holomorphic function Relatively compact Several complex variables Mathematics Elsevier Function of several complex variables Bergman–Weil formula Complex coordinate space Domain of holomorphy Oka–Weil theorem Englewood Cliffs Springer-Verlag Istituto Nazionale di Alta Matematica Prentice-Hall Weil domain dbr:Mario_Benedicty dbr:Universitatis_Iagellonicae_Acta_Mathematica
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=L0zJmamx5AAC https://books.google.com/books%3Fid=nDgBsOurnAIC https://archive.org/details/severalcomplexva0000unse/page/19 http://www.emis.de/journals/UIAM/PDF/45-139-145.pdf
sameAs	Analytic polyhedron Analytic polyhedron Analytic polyhedron Analytic polyhedron Analytic polyhedron
dbp:wikiPageUsesTemplate	dbt:Citation dbt:ISBN dbt:Math dbt:Reflist dbt:Mathanalysis-stub
has abstract	In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space Cn of the form where D is a bounded connected open subset of Cn, are holomorphic on D and P is assumed to be relatively compact in D. 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. (en) Analytisk polyeder förekommer inom komplex analys (som är ett forskningsfält inom matematiken) och avser ett geometriskt objekt, ett speciellt slag av (öppet) område i ett flerdimensionellt komplext vektorrum, eller mer generellt i en komplex mångfald. Analytiska polyedrar är av intresse för sin speciella geometri och kanske mest för de analytiska egenskaper som objekt förknippade med dem därmed har. (sv)
prov:wasDerivedFrom	wikipedia-en:Analytic_polyhedron?oldid=1059743376&ns=0
page length (characters) of wiki page	5074 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Analytic_polyhedron
is Link from a Wikipage to another Wikipage of	Behnke–Stein theorem on Stein manifolds Pseudoconvexity Function of several complex variables Bergman–Weil formula Domain (mathematical analysis) Polynomial polyhedron
is Wikipage redirect of	Polynomial polyhedron
is foaf:primaryTopic of	wikipedia-en:Analytic_polyhedron

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