domain of holomorphy

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• Domain of holomorphy — The sets in the definition. In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a set which is maximal in the sense that there exists a holomorphic function on this set which cannot be extended to a… …   Wikipedia

• Analytic continuation — In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where …   Wikipedia

• List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… …   Wikipedia

• Holomorphically convex hull — In mathematics, more precisely in complex analysis, the holomorphically convex hull of a given compact set in the n dimensional complex space C n is defined as follows. Let G subset {mathbb{C^n be a domain (an open and connected set), or… …   Wikipedia

• Jordan matrix — In the mathematical discipline of matrix theory, a Jordan block over a ring R (whose identities are the zero 0 and one 1) is a matrix which is composed of 0 elements everywhere except for the diagonal, which is filled with a fixed element… …   Wikipedia

• Hartogs' extension theorem — In mathematics, precisely in the theory of functions of several complex variables, Hartogs extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that the support of the… …   Wikipedia

• Mittag-Leffler star — Illustration of the Mittag Leffler star (the region bounded by the blue contour). The original disk U is centered at a. In complex analysis, a branch of mathematics, the Mittag Leffler star of a complex analytic function is a set in the… …   Wikipedia

• Prolongement analytique — En analyse complexe, la théorie du prolongement analytique détaille l ensemble des propriétés et techniques concernant le prolongement des fonctions holomorphes (ou analytiques). Elle considère d abord la question du prolongement dans le plan… …   Wikipédia en Français

• Identity theorem — In complex analysis, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a connected open set D , if f = g on some neighborhood of z that is in D , then f = g on D . Thus a holomorphic function is… …   Wikipedia

• Antiderivative (complex analysis) — In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex valued function g is a function whose complex derivative is g. More precisely, given an open set U in the complex plane and a function the antiderivative …   Wikipedia

• Holomorphic function — A rectangular grid (top) and its image under a holomorphic function f (bottom). In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex valued function of one or more complex …   Wikipedia