Search results

{{short description|Space formed by the ''n''-tuples of complex numbers}} ...and is the ''n''-fold [[Cartesian product]] of the [[complex line]] <math>\Complex</math> with itself. Symbolically, ...

{{Short description|Proposition in complex analysis introduced by William Fogg Osgood}} ...complex analysis]]. It states that a [[continuous function]] of several [[complex variable]]s that is [[holomorphic function|holomorphic]] in each variable s ...

{{Short description|Theorem in complex analysis about the sheaf of holomorphic functions}} ...tly the sheaf <math>\mathcal{O}_{X}</math> of holomorphic functions on a [[complex manifold]] <math>X</math>) is [[coherent sheaf|coherent]].<ref>{{harvtxt|No ...

...matics, especially [[Function of several complex variables|several complex variables]], the '''Behnke–Stein theorem''' states that a union of an increasing sequ [[Category:Several complex variables]] ...

In [[several complex variables]], '''Hefer's theorem''' is a result that represents the difference at two ...Complex^n</math> be a [[domain of holomorphy]] and <math>f:\Omega\mapsto \Complex</math> be a [[holomorphic function]]. Then, there exist holomorphic functio ...

In the [[mathematics|mathematical]] study of [[several complex variables]], the '''Szegő kernel''' is an [[integral kernel]] that gives rise to a [[ ...ven G. | authorlink=Steven Krantz|title=Function Theory of Several Complex Variables | publisher=[[American Mathematical Society]] | location=Providence, R.I. | ...

* In [[Function of several complex variables|several complex variables]]:<ref>{{cite book | title = Analytic Functions of Several Complex Variables ...

...ally the theory of [[Function of several complex variables|several complex variables]], the '''Oka–Weil theorem''' is a result about the [[uniform convergence]] ...az |editor2-first=Michael Th. |editor2-last=Rassias |title=Advancements in Complex Analysis – Holomorphic Approximation |chapter=The Legacy of Weierstrass, Ru ...

In mathematics, particularly in the study of functions of [[several complex variable]]s, '''Ushiki's theorem''', named after S.&nbsp;Ushiki, states tha ...Sci. Paris, 291(7):447–449, 1980</ref> The theorem appeared in print again several years later, in a certain Russian journal, by an author apparently unaware ...

{{short description|Subset of complex n-space bounded by analytic functions}} ...an '''analytic polyhedron''' is a subset of the [[Complex coordinate space|complex space]] {{math|'''C'''^''n''}} of the form ...

...]], a branch of mathematics, the '''residue at infinity''' is a [[Residue (complex analysis)|residue]] of a [[holomorphic function]] on an [[Annulus (mathemat * Murray R. Spiegel, ''Variables complexes'', Schaum, {{isbn|2-7042-0020-3}} ...

{{Short description|Class of complex vector function}} ...k'' and index ''m'' is a function <math>\phi(\tau,z)</math> of two complex variables (with &tau; in the upper half plane) such that ...

...t \geq 0 </math> and <math> h > 0 </math>, the distribution of the random variables ...he <math> X_t </math> are [[independent and identically distributed random variables]] following a [[normal distribution]] with mean zero and variance one. Then ...

{{Short description|Theorem about holomorphic functions of several complex variables}} ...t1=Bochner | first1=S. | last2=Martin | first2=W.T.| title=Several Complex Variables | publisher=Princeton University Press | series=Princeton mathematical seri ...

......,&nbsp;''z''_''n'') is a [[polynomial]] with [[complex number|complex]] coefficients, and that it is * symmetric, i.e. invariant under [[permutation]]s of the variables, and ...

...is an American mathematician who works on the theory of [[several complex variables]]. He solved a boundary behavior problem of complex analysis in several variables, on which his teacher Kohn worked in detail and which was originally formul ...

...number]] in a [[Domain (mathematical analysis)|domain]] <math>R\subseteq \Complex</math>. The operator <math>\bar{\partial}</math> is called the DBAR operato The DBAR operator is nothing other than the complex conjugate of the operator ...

...e [[Joint probability distribution|joint distribution]] of two real random variables. ...of a complex random variable. Other concepts are unique to complex random variables. ...

In mathematics, specifically in [[complex analysis]], '''Cauchy's estimate''' gives local bounds for the [[derivative where <math>f^{(n)}</math> is the ''n''-th [[complex derivative]] of <math>f</math>; i.e., <math>f' = \frac{\partial f}{\partial ...

...ma is the inverse of Levi's problem (unramified Riemann domain over <math>\Complex^n</math>). Perhaps, this is why Oka referred to Levi's problem as "problème | title = Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique intérieur ...