Introduction to Abstract Harmonic Analysis
E639088
Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Introduction to Abstract Harmonic Analysis canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7047107 — 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: Introduction to Abstract Harmonic Analysis Context triple: [Lynn Harold Loomis, notableWork, Introduction to Abstract Harmonic Analysis]
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A.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
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B.
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
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C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
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D.
Lectures on Fourier Integrals
Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
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E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
- 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: Introduction to Abstract Harmonic Analysis Target entity description: Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
-
A.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
-
B.
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
-
C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
-
D.
Lectures on Fourier Integrals
Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
-
E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
- F. None of above. chosen
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
textbook ⓘ |
| audience |
graduate students in mathematics
ⓘ
researchers in functional analysis ⓘ researchers in harmonic analysis ⓘ |
| educationalLevel | graduate ⓘ |
| emphasis |
abstract formulation of harmonic analysis
ⓘ
topological and measure-theoretic aspects of groups ⓘ |
| field |
abstract harmonic analysis
ⓘ
functional analysis ⓘ harmonic analysis ⓘ topological groups ⓘ |
| focus |
systematic development of harmonic analysis on abstract structures
ⓘ
theory of harmonic analysis on topological groups ⓘ |
| genre |
mathematics textbook
ⓘ
reference work ⓘ |
| hasPrerequisite |
basic functional analysis
ⓘ
measure theory ⓘ real analysis ⓘ |
| purpose |
to introduce abstract harmonic analysis on topological groups
ⓘ
to provide a rigorous foundation for harmonic analysis on groups ⓘ |
| structure | systematic development of theory ⓘ |
| topic |
Banach algebras associated with groups
ⓘ
Fourier series and Fourier integrals in abstract settings ⓘ Fourier transform on groups ⓘ Haar measure ⓘ Pontryagin duality ⓘ characters of locally compact abelian groups ⓘ convolution on groups ⓘ harmonic analysis on topological groups ⓘ locally compact abelian groups ⓘ representation theory of groups ⓘ unitary representations ⓘ |
| usedIn |
graduate courses in abstract harmonic analysis
ⓘ
graduate courses in functional analysis ⓘ graduate courses in harmonic analysis ⓘ |
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: Introduction to Abstract Harmonic Analysis Description of subject: Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.