Hurwitz's theorem (complex analysis)
GPTKB entity
Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
holomorphic functions
sequences of functions |
| gptkbp:category |
theorems in complex analysis
|
| gptkbp:field |
complex analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hurwitz's theorem (complex analysis)
|
| gptkbp:implies |
Zeros of the limit function are approximated by zeros of the sequence
|
| gptkbp:namedAfter |
gptkb:Adolf_Hurwitz
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Montel's_theorem
gptkb:Rouché's_theorem |
| gptkbp:sentence |
If a sequence of holomorphic functions converges uniformly on compact subsets to a non-constant holomorphic function, then the zeros of the limit function are limits of zeros of the sequence.
|
| gptkbp:year |
1889
|
| gptkbp:bfsParent |
gptkb:Adolf_Hurwitz
|
| gptkbp:bfsLayer |
5
|