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・ Analytic frame
・ Analytic Fredholm theorem
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Analytic polyhedron
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Analytic polyhedron : ウィキペディア英語版
Analytic polyhedron
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 f_j are holomorphic on .〔See and .〕 If f_j 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 the union of the set of hypersurfaces
: \sigma_j = \, 1 \le j \le N.
An analytic polyhedron is a ''Weil polyhedron'', or Weil domain if the intersection of hypersurfaces has dimension no greater than .〔.〕
==See also==

*Behnke–Stein theorem
*Bergman–Weil formula

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