Inequalities for analytic functions
E451538
"Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Analytic Functions | 1 |
| Inequalities for analytic functions canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4552550 — 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: Inequalities for analytic functions Context triple: [Gábor Szegő, notableWork, Inequalities for analytic functions]
-
A.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
-
B.
Hadamard three-circle theorem
The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
-
C.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
D.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
E.
Schwarz lemma
Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
- 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: Inequalities for analytic functions Target entity description: "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
-
A.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
-
B.
Hadamard three-circle theorem
The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
-
C.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
D.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
E.
Schwarz lemma
Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical work
ⓘ
research monograph ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| associatedWith |
20th-century mathematics
ⓘ
Hungarian mathematical school ⓘ
linked to:
Hungarian school of combinatorics
|
| author | Gábor Szegő ⓘ |
| contributesTo |
approximation theory of analytic functions
ⓘ
classical complex analysis ⓘ theory of analytic function inequalities ⓘ |
| contributor | Gábor Szegő ⓘ |
| field |
approximation theory
ⓘ
complex analysis ⓘ mathematics ⓘ |
| focusesOn |
boundary behavior of analytic functions
ⓘ
coefficient estimates ⓘ complex-valued analytic functions ⓘ extremal problems in complex analysis ⓘ growth of analytic functions ⓘ maximum modulus estimates ⓘ orthogonal polynomials ⓘ polynomial approximation ⓘ |
| genre | mathematics book ⓘ |
| hasInfluenceOn |
later work on extremal problems for analytic functions
ⓘ
research on bounds for polynomials and power series ⓘ |
| language | English ⓘ |
| mainSubject |
analytic functions
ⓘ
bounds for analytic functions ⓘ estimates for analytic functions ⓘ inequalities ⓘ |
| relatedTo |
Bernstein-type inequalities
ⓘ
Cauchy estimates for derivatives ⓘ Fourier series of analytic functions ⓘ Hadamard three-circle theorem ⓘ Jensen’s formula ⓘ Markov-type inequalities ⓘ maximum modulus principle ⓘ orthogonal polynomials on the unit circle ⓘ |
| usedIn |
graduate-level study of complex analysis
ⓘ
research in approximation theory ⓘ research on extremal analytic problems ⓘ |
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: Inequalities for analytic functions Description of subject: "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Inequalities for analytic functions