The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space C n {\displaystyle...

analytic functions of a complex variable, that is, holomorphic functions. The concept can be extended to functions of several complex variables. Complex analysis...

idea of a function of a real variable to several variables. The "input" variables take real values, while the "output", also called the "value of the function"...

holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in...

function of several real variables or of a function of several complex variables. There are various standard ways for denoting functions. The most commonly...

theory of functions of several complex variables, Hartogs's extension theorem is a statement about the singularities of holomorphic functions of several variables...

1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which...

coordinate separately. Several complex variables is the study of such holomorphic functions in n variables. More generally, the complex n-space is the target space...

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...

))={\mathfrak {c}}} . Real analysis Function of several real variables Complex analysis Function of several complex variables R. Courant (23 February 1988)...

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...

convex-(down), function. Many properties of convex functions have the same simple formulation for functions of many variables as for functions of one variable. See...

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces...

analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at...

work on partial differential equations and on the theory of functions of several complex variables. Lewy was born to a Jewish family in Breslau, Silesia...

Clarita Valley, California, US Function of several complex variables, This field of mathematics is called several complex variables and is often abbreviated...

concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions...

Analytic functions of several variables have some of the same properties as analytic functions of one variable. However, especially for complex analytic...

proposition in complex analysis. It states that a continuous function of several complex variables that is holomorphic in each variable separately is holomorphic...

theory of special functions, because such elliptic functions, or abelian functions of several complex variables, are then 'very special' functions satisfying...

commonly interpreted as real variables, but the formulas remain valid if the variables are interpreted as complex variables. These formulas may be used...

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

function in Wiktionary, the free dictionary. Theta functions ϑ ( z ; τ ) {\displaystyle \vartheta (z;\tau )} are special functions of several complex...

complesse" [The contributions of Guido Fubini and Francesco Severi to the theory of functions of several complex variables], Atti del convegno matematico...

with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep...

distribution functions are also used to specify the distribution of multivariate random variables. The cumulative distribution function of a real-valued...

properties of the gamma function. Although Euler was a pioneer in the theory of complex variables, he does not appear to have considered the factorial of a complex...

examples include Robert Gunning and Hugo Rossi's Analytic Functions of Several Complex Variables (1965) and Lynn Loomis and Shlomo Sternberg's Advanced Calculus...

"Chapter III. Variety (Sec. B. Anlytic cover)". Analytic Functions of Several Complex Variables. American Mathematical Soc. ISBN 9780821821657. Gunning...

problem is at a deeper level of abstraction, because it is much harder to manipulate analytic functions of several complex variables. The formal definition...