Lindelöf theorem in complex analysis

E518479

theorem in complex analysis

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.

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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 ⓘ linked to: Ernst Lindelöf
refines	maximum modulus principle ⓘ
relatedTo	Fatou theorem ⓘ Phragmén–Lindelöf principle ⓘ boundary uniqueness theorems ⓘ maximum modulus principle ⓘ
typicalDomain	unit disk ⓘ upper half-plane ⓘ
usedIn	Hardy space theory ⓘ linked to: Hardy space boundary value problems in complex analysis ⓘ geometric function theory ⓘ theory of univalent functions ⓘ
usesConcept	Phragmén–Lindelöf principle ⓘ Stolz angles ⓘ angular limits ⓘ maximum modulus principle ⓘ nontangential limits ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Ernst Lindelöf → notableFor → Lindelöf theorem in complex analysis ⓘ

Ernst Lindelöf → hasConceptNamedAfter → Lindelöf theorem ⓘ

linked to: Lindelöf theorem in complex analysis

Hadamard three-circle theorem → relatedTo → Phragmén–Lindelöf principle ⓘ