In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a domain which is maximal in the sense that there exists...

{C} } ), is the domain of holomorphy of some function, in other words every domain has a function for which it is the domain of holomorphy. For several complex...

defined Domain of definition of a partial function Natural domain of a partial function Domain of holomorphy of a function Domain of an algebraic structure...

appropriate integrability properties. Tubes over convex sets are domains of holomorphy. The Hardy spaces on tubes over convex cones have an especially...

sets are domains of holomorphy. The characterization of domains of holomorphy leads to the notion of pseudoconvexity. Cauchy–Riemann equations Holomorphic...

extended to larger domains are highly limited. Such a set is called a domain of holomorphy. A complex differential ⁠ ( p , 0 ) {\displaystyle (p,0)} ⁠-form...

natural boundary if all points are singular, in which case the domain is a domain of holomorphy. For ℜ ( s ) > 1 {\displaystyle \Re (s)>1} we define the so-called...

notion of this Hartogs's extension theorem and the domain of holomorphy. Let f be a holomorphic function on a set G \ K, where G is an open subset of Cn (n...

\subseteq \mathbb {C} } ; that is, the spectrum of the matrix is contained inside the domain of holomorphy of f. Let f ( z ) = ∑ h = 0 ∞ a h ( z − z 0 ) h...

to describe pseudoconvex domains, domains of holomorphy and Stein manifolds. The main geometric application of the theory of plurisubharmonic functions...

mathematics, infinite-dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to...

complex variables, where the problem of determining what kind of hypersurface can be the boundary of a domain of holomorphy. Levi, Eugenio Elia (1911), "Sulle...

solution of the second Cousin problem. The standard complex space C n {\displaystyle \mathbb {C} ^{n}} is a Stein manifold. Every domain of holomorphy in C...

is the full group of isometries for the Teichmüller metric. The Bers embedding realises Teichmüller space as a domain of holomorphy and hence it also...

extension theorem) and the concepts of holomorphic hull and domain of holomorphy. In set theory, he contributed to the theory of well-orders and proved what is...

they allow for classification of domains of holomorphy. Let G ⊂ C n {\displaystyle G\subset {\mathbb {C} }^{n}} be a domain, that is, an open connected...

mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in C n {\displaystyle \mathbb {C} ^{n}} , the function − log ⁡ d...

and second Cousin problems, and work on domains of holomorphy, in the period 1936–1940. He received his Doctor of Science degree from Kyoto Imperial University...

f^{(m)}(c)\neq g^{(m)}(c)} . By holomorphy, we have the following Taylor series representation in some open neighborhood U of c {\displaystyle c} : ( f −...

the Mittag-Leffler star of some complex-analytic function, since any open set in the complex plane is a domain of holomorphy. Any complex-analytic function...

k + 1 {\displaystyle G_{k}\subset G_{k+1}} ) of domains of holomorphy is again a domain of holomorphy. It was proved by Heinrich Behnke and Karl Stein...

(including infinite-dimensional holomorphy, integral transforms in distribution spaces) 47: Operator theory 49: Calculus of variations and optimal control;...

structure sheaf of a complex-analytic space (e.g., a complex manifold) is coherent. Every complex affine space is a domain of holomorphy. In particular...

tube is a domain of holomorphy" (PDF). Mathematical Research Letters. 5 (2): 185–190. doi:10.4310/MRL.1998.v5.n2.a4. "周向宇 (with CV & list of "Representative...

number. Levi Levi's problem asks to show a pseudoconvex set is a domain of holomorphy. line integral Line integral. Liouville Liouville's theorem says...

of functions of several complex variables, where the problem of determining what kind of hypersurface can be the boundary of a domain of holomorphy....

Notices of the AMS. 50: 554–555. Fornaess, John Erik; Diederich, Klas (1976). "A strange bounded smooth domain of holomorphy". Bulletin of the American...

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...

polyhedron domain used in the proof of the Behnke–Stein theorem on domains of holomorphy and the Oka–Weil theorem. Heinrich Behnke & Karl Stein (1948), "Entwicklung...

una variabile complessa" [A fundamental property of the domain of holomorphy of an analytic function of one real variable and one complex variable], Rendiconti...