- Fields of mathematics
- >
- Mathematical analysis
- >
- Functions and mappings
- >
- Several complex variables

- Mathematical analysis
- >
- Fields of mathematical analysis
- >
- Complex analysis
- >
- Several complex variables

- Mathematical analysis
- >
- Mathematical relations
- >
- Functions and mappings
- >
- Several complex variables

- Mathematical concepts
- >
- Mathematical objects
- >
- Functions and mappings
- >
- Several complex variables

- Mathematical concepts
- >
- Mathematical relations
- >
- Functions and mappings
- >
- Several complex variables

- Philosophy of mathematics
- >
- Mathematical objects
- >
- Functions and mappings
- >
- Several complex variables

- Predicate logic
- >
- Mathematical relations
- >
- Functions and mappings
- >
- Several complex variables

Symmetric cone

In mathematics, symmetric cones, sometimes called domains of positivity, are open convex self-dual cones in Euclidean space which have a transitive group of symmetries, i.e. invertible operators that

Hartogs's theorem on separate holomorphicity

In mathematics, Hartogs's theorem is a fundamental result of Friedrich Hartogs in the theory of several complex variables. Roughly speaking, it states that a 'separately analytic' function is continuo

Ohsawa–Takegoshi L2 extension theorem

In several complex variables, the Ohsawa–Takegoshi L2 extension theorem is a fundamental result concerning the holomorphic extension of an -holomorphic function defined on a bounded Stein manifold (su

Szegő kernel

In the mathematical study of several complex variables, the Szegő kernel is an integral kernel that gives rise to a reproducing kernel on a natural Hilbert space of holomorphic functions. It is named

Biholomorphism

In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose i

Plurisubharmonic function

In mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis. On a Kähler manifold, plurisubharmoni

Andreotti–Norguet formula

The Andreotti–Norguet formula, first introduced by Aldo Andreotti and , is a higher–dimensional analogue of Cauchy integral formula for expressing the derivatives of a holomorphic function. Precisely,

Complex geometry

In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the stud

Ushiki's theorem

In mathematics, particularly in the study of functions of several complex variables, Ushiki's theorem, named after S. Ushiki, states that certain well-behaved functions cannot have certain kinds of we

Tube domain

In mathematics, a tube domain is a generalization of the notion of a vertical strip (or half-plane) in the complex plane to several complex variables. A strip can be thought of as the collection of co

Cousin problems

In mathematics, the Cousin problems are two questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced in

Polar homology

In complex geometry, a polar homology is a group which captures holomorphic invariants of a complex manifold in a similar way to usual homology of a manifold in differential topology. Polar homology w

Behnke–Stein theorem

In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence (i.e., ) of domains of holomorphy is again a domain of holomorphy. It was p

Behnke–Stein theorem on Stein manifolds

In mathematics, especially several complex variables, the Behnke–Stein theorem states that a connected, non-compact (open) Riemann surface is a Stein manifold. In other words, it states that there is

Positive current

In mathematics, more particularly in complex geometry,algebraic geometry and complex analysis, a positive currentis a positive (n-p,n-p)-form over an n-dimensional complex manifold,taking values in di

Bergman kernel

In the mathematical study of several complex variables, the Bergman kernel, named after Stefan Bergman, is the reproducing kernel for the Hilbert space (RKHS) of all square integrable holomorphic func

Edge-of-the-wedge theorem

In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the

Suita conjecture

In mathematics, the Suita conjecture is a conjecture related to the theory of the Riemann surface, the boundary behavior of conformal maps, the theory of Bergman kernel, and the theory of the L2 exten

Domain 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 a holomorphic function on this domain which

Analytic polyhedron

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

Weierstrass preparation theorem

In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplicat

Bombieri norm

In mathematics, the Bombieri norm, named after Enrico Bombieri, is a norm on homogeneous polynomials with coefficient in or (there is also a version for non homogeneous univariate polynomials). This n

Poincaré residue

In mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory. It is just one of a number of s

Bochner–Martinelli formula

In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced by Enzo Martinelli and Salomon Bochner.

Complex coordinate space

In mathematics, the n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers. It is denoted , and is the n-fold Cartesian product of the comple

Bergman–Weil formula

In mathematics, the Bergman–Weil formula is an integral representation for holomorphic functions of several variables generalizing the Cauchy integral formula. It was introduced by and .

Complex analytic variety

In mathematics, and in particular differential geometry and complex geometry, a complex analytic variety or complex analytic space is a generalization of a complex manifold which allows the presence o

Skoda–El Mir theorem

The Skoda–El Mir theorem is a theorem of complex geometry, stated as follows: Theorem (Skoda, El Mir, Sibony). Let X be a complex manifold, and E a closed complete pluripolar set in X. Consider a clos

Hartogs's extension theorem

In the theory of functions of several complex variables, Hartogs's extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that th

Polydisc

In the theory of functions of several complex variables, a branch of mathematics, a polydisc is a Cartesian product of discs. More specifically, if we denote by the open disc of center z and radius r

Cartan's theorems A and B

In mathematics, Cartan's theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf F on a Stein manifold X. They are significant both as applied to several compl

Bochner's tube theorem

In mathematics, Bochner's tube theorem (named for Salomon Bochner) shows that every function holomorphic on a tube domain in can be extended to the convex hull of this domain. Theorem Let be a connect

Bateman transform

In the mathematical study of partial differential equations, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral o

Oka–Weil theorem

In mathematics, especially the theory of several complex variables, the Oka–Weil theorem is a result about the uniform convergence of holomorphic functions on Stein spaces due to Kiyoshi Oka and André

Theta function

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann

Pseudoconvexity

In mathematics, more precisely in the theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn. Pseudoconvex sets are im

Pluriharmonic function

In mathematics, precisely in the theory of functions of several complex variables, a pluriharmonic function is a real valued function which is locally the real part of a holomorphic function of severa

Fatou–Bieberbach domain

In mathematics, a Fatou–Bieberbach domain is a proper subdomain of , biholomorphically equivalent to . That is, an open set is called a Fatou–Bieberbach domain if there exists a bijective holomorphic

Holomorphic separability

In mathematics in complex analysis, the concept of holomorphic separability is a measure of the richness of the set of holomorphic functions on a complex manifold or complex-analytic space.

Malgrange–Zerner theorem

In mathematics, Malgrange–Zerner theorem (named for Bernard Malgrange and ) shows that a function on allowing holomorphic extension in each variable separately can be extended, under certain condition

Function of several complex variables

The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several comple

Thin set (analysis)

In mathematical analysis, a thin set is a subset of n-dimensional complex space Cn with the property that each point has a neighbourhood on which some non-zero holomorphic function vanishes. Since the

© 2023 Useful Links.