Harmonic Analysis on Homogeneous Spaces
E893438
Harmonic Analysis on Homogeneous Spaces is a mathematical monograph by Nolan Wallach that develops the theory of harmonic analysis and representation theory on Lie groups and their homogeneous spaces.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Harmonic Analysis on Homogeneous Spaces canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10931404 — 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: Harmonic Analysis on Homogeneous Spaces Context triple: [Nolan Wallach, hasWrittenWork, Harmonic Analysis on Homogeneous Spaces]
-
A.
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.
-
B.
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.
-
C.
Introduction to Abstract Harmonic Analysis
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.
-
D.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
E.
Paley–Wiener theorem for real reductive groups
The Paley–Wiener theorem for real reductive groups is a fundamental result in harmonic analysis that characterizes the image of compactly supported smooth functions under the group Fourier transform in terms of holomorphic functions with specific growth and support conditions.
- 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: Harmonic Analysis on Homogeneous Spaces Target entity description: Harmonic Analysis on Homogeneous Spaces is a mathematical monograph by Nolan Wallach that develops the theory of harmonic analysis and representation theory on Lie groups and their homogeneous spaces.
-
A.
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.
-
B.
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.
-
C.
Introduction to Abstract Harmonic Analysis
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.
-
D.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
E.
Paley–Wiener theorem for real reductive groups
The Paley–Wiener theorem for real reductive groups is a fundamental result in harmonic analysis that characterizes the image of compactly supported smooth functions under the group Fourier transform in terms of holomorphic functions with specific growth and support conditions.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| author |
Nolan R. Wallach
ⓘ
linked to:
Nolan Wallach
|
| contribution |
integration of representation theory with harmonic analysis on homogeneous spaces
ⓘ
systematic development of harmonic analysis on Lie groups and homogeneous spaces ⓘ |
| field |
Lie theory
ⓘ
harmonic analysis ⓘ representation theory ⓘ |
| genre | advanced mathematics text ⓘ |
| hasSubjectArea |
abstract harmonic analysis
ⓘ
functional analysis ⓘ pure mathematics ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| language | English ⓘ |
| relatedTo |
Harish-Chandra’s work on semisimple Lie groups
ⓘ
Representation Theory of Lie Groups ⓘ
linked to:
Representations of groups
|
| topic |
Cartan decomposition
ⓘ
Fourier analysis on Lie groups ⓘ Gelfand pairs ⓘ Harish-Chandra theory ⓘ Iwasawa decomposition ⓘ Lie groups ⓘ Plancherel theorem ⓘ characters of representations ⓘ compact Lie groups ⓘ discrete series representations ⓘ eigenfunction expansions ⓘ homogeneous spaces ⓘ induced representations ⓘ invariant differential operators ⓘ matrix coefficients of representations ⓘ non-compact Lie groups ⓘ parabolic subgroups ⓘ principal series representations ⓘ reductive Lie groups ⓘ
linked to:
reductive Lie group
semisimple Lie groups ⓘ spherical functions ⓘ symmetric spaces ⓘ unitary representations of Lie groups ⓘ |
| usedIn |
research on automorphic forms
ⓘ
research on number theory related to Lie groups ⓘ |
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: Harmonic Analysis on Homogeneous Spaces Description of subject: Harmonic Analysis on Homogeneous Spaces is a mathematical monograph by Nolan Wallach that develops the theory of harmonic analysis and representation theory on Lie groups and their homogeneous spaces.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.