Explore: Domains Of Holomorphy

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

case; there exist domains ( D ⊂ C n ,   n ≥ 2 {\displaystyle D\subset \mathbb {C} ^{n},\ n\geq 2} ) that are not the domain of holomorphy of any function,

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

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

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

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

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

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

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

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