Lindelöf theorem in complex analysis
E518479
The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Lindelöf theorem | 1 |
| Lindelöf theorem in complex analysis canonical | 1 |
| Phragmén–Lindelöf principle | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5425836 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lindelöf theorem in complex analysis Context triple: [Ernst Lindelöf, notableFor, Lindelöf theorem in complex analysis]
-
A.
Mittag-Leffler theorem
The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
-
B.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
-
C.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
-
D.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
-
E.
Riemann mapping theorem
The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lindelöf theorem in complex analysis Target entity description: The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
-
A.
Mittag-Leffler theorem
The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
-
B.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
-
C.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
-
D.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
-
E.
Riemann mapping theorem
The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
- F. None of above. chosen
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf | theorem in complex analysis ⓘ |
| appliesTo |
functions analytic in simply connected domains
ⓘ
functions analytic in the unit disk ⓘ functions bounded in a domain ⓘ |
| assumes |
analyticity in a domain
ⓘ
boundedness or controlled growth of the function ⓘ |
| category |
growth theorem in complex analysis
ⓘ
theorem about boundary behavior ⓘ |
| concerns |
analytic functions
ⓘ
boundary behavior of analytic functions ⓘ growth of analytic functions near the boundary ⓘ holomorphic functions ⓘ |
| concludes |
control of the modulus of the function near boundary points
ⓘ
existence of certain boundary limits under growth conditions ⓘ |
| controls |
boundary growth of analytic functions
ⓘ
growth along curves approaching boundary points ⓘ |
| describes | asymptotic behavior of analytic functions along approach paths to boundary points ⓘ |
| field | complex analysis ⓘ |
| historicalPeriod | early 20th century ⓘ |
| implies |
growth estimates along nontangential approach regions
ⓘ
restrictions on possible boundary singularities of analytic functions ⓘ |
| namedAfter | Ernst Leonard Lindelöf NERFINISHED ⓘ |
| refines | maximum modulus principle NERFINISHED ⓘ |
| relatedTo |
Fatou theorem
NERFINISHED
ⓘ
Phragmén–Lindelöf principle NERFINISHED ⓘ boundary uniqueness theorems ⓘ maximum modulus principle ⓘ |
| typicalDomain |
unit disk
ⓘ
upper half-plane ⓘ |
| usedIn |
Hardy space theory
NERFINISHED
ⓘ
boundary value problems in complex analysis ⓘ geometric function theory ⓘ theory of univalent functions ⓘ |
| usesConcept |
Phragmén–Lindelöf principle
NERFINISHED
ⓘ
Stolz angles NERFINISHED ⓘ angular limits ⓘ maximum modulus principle ⓘ nontangential limits ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lindelöf theorem in complex analysis Description of subject: The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Lindelöf theorem
this entity surface form:
Phragmén–Lindelöf principle