Search results

{{Short description|Theorem in complex analysis about the sheaf of holomorphic functions}} ...h>) is [[coherent sheaf|coherent]].<ref>{{harvtxt|Noguchi|2019}}</ref><ref>In {{harvtxt|Oka|1950}} paper it was called the [[idéal de domaines indétermin ...

...heorem was originally formulated by [[Giulio Vivanti ]] in 1893 and proved in the following year by [[Alfred Pringsheim]]. A complex function defined by a [[power series]] ...

In mathematics, the '''Grace–Walsh–Szegő coincidence theorem'''<ref>{{cite jou ......,&nbsp;''z''_''n'') is a [[polynomial]] with [[complex number|complex]] coefficients, and that it is ...

...ty Press]]|isbn=9781400858682|pages=68|language=en}}</ref> Given a compact complex manifold ''M'' with a [[holomorphic line bundle]] ''F'' over ''M'', the Nak ...first2=Shigeo|date=1954|title=Note on Kodaira-Spencer's proof of Lefschetz theorems|url=https://projecteuclid.org/euclid.pja/1195526105|journal=Proceedings of ...

...ison matrix''' {{math|1=''M''(''A'')&nbsp;=&nbsp;(''α_ij'')}} of complex matrix ''A'' is defined as ...55-1 |edition=2nd |page=92 |chapter=Basic Iterative Methods and Comparison Theorems}}</ref> ...

...tion (mathematics)|characterizes]] the [[gamma function]], defined for all complex numbers <math>z</math> for which <math>\mathrm{Re}\,z > 0</math> by ...nly function <math>f</math> defined on the half-plane <math>H := \{ z \in \Complex : \operatorname{Re}\,z > 0\}</math> such that: ...

...n of [[Mergelyan's theorem]] from compact subsets of an open subset of the complex plane to relatively closed subsets of an open subset. Let Ω be an open subset of <math>\Complex</math> and ''E'' a relatively closed subset of Ω. By Ω^* is denot ...

{{Short description|Proposition in complex analysis introduced by William Fogg Osgood}} ...several [[complex variable]]s that is [[holomorphic function|holomorphic]] in each variable separately is holomorphic. The assumption that the function i ...

'''Matsaev's theorem''' is a theorem from [[complex analysis]], which characterizes the [[Entire function#Order and type|order and type] The theorem was proven in 1960 by [[Vladimir Igorevich Matsaev]].<ref>{{cite journal|first1=Wladimir ...

...rtogs]] and [[Arthur Rosenthal]] and has been widely applied, particularly in [[operator theory]]. ...t of the complex plane with [[Lebesgue measure]] zero, then any continuous complex-valued function on ''K'' can be uniformly approximated by rational function ...

...or simple roots of a function. In particular, it has numerous applications in [[Root-finding algorithm|root finding algorithms]] like [[Newton's method]] which only has one simple pole <math>x=r</math> in this disk. Then ...

...}}</ref> Moreover, the isomorphism respects the [[monodromy operator]]s in the sense: <math>T_{f_1} \otimes T_{f_2} = T_f</math>.<ref name="Illusie">{ The theorem was introduced by [[René Thom|Thom]] and Sebastiani in 1971.<ref>{{cite journal |last1=Sebastiani |first1=M. |last2=Thom |first2=R ...

...e surface of the unit disc <math>\left.\right.\{z:|z|<1\} </math> of the [[complex plane]], along with a form of the [[orthogonal projection]] from <math>\lef }}</ref> contains the following theorem presented also in [[Joseph L. Walsh]]'s well-known monograph ...

...ly continuous operator|first1=Victor I.|last1=Lomonosov|journal=Functional Analysis and Its Applications|volume=7|pages=213–214|date=1973|issue=3 |doi=10.1007/ ...if <math>T(M)\subset M</math>, i.e. <math>Tx\in M</math> for every <math>x\in M</math>. ...

...the conditions stated below, [[integrable]] functions can be approximated in L¹ from above and below by lower- and [[upper-semicontinuous]] f | title = Real and Complex Analysis ...

{{Short description|Theorem in mathematics about unions of domains of holomorphy}} ...roved by [[Heinrich Behnke]] and [[Karl Stein (mathematician)|Karl Stein]] in 1938.<ref>{{cite journal |last1=Behnke |first1=H. |authorlink1=Heinrich Beh ...

In mathematics, particularly in the study of functions of [[several complex variable]]s, '''Ushiki's theorem''', named after S.&nbsp;Ushiki, states tha ...ompact space|compact]] [[smooth function|smooth]] [[invariant manifold]]. In particular, such a map cannot have a [[homoclinic connection]] or [[heteroc ...

...50px|right|Counterexample to a strengthening of the uniform limit theorem, in which pointwise convergence, rather than uniform convergence, is assumed. T In [[mathematics]], the '''uniform limit theorem''' states that the [[uniform ...

In the [[mathematics|mathematical]] field of [[complex analysis]], '''Akhiezer's theorem''' is a result about [[entire function]]s proved b ...</math>, of [[exponential type]] <math>\tau/2</math>, having all its zeros in the (closed) upper half plane, such that ...

...oes not take the values 0 or 1, the value of |''f''(''z'')| can be bounded in terms of ''z'' and ''f''(0). ...em B}} gave a strong explicit bound, showing that if ''f'' is holomorphic in the open unit disk and does not take the values 0 or 1, then ...