Generalized Functions (multi-volume series)
E270391
Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T2475546 — 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: Generalized Functions (multi-volume series) Context triple: [Israel Gelfand, notableWork, Generalized Functions (multi-volume series)]
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A.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
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B.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
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C.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
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D.
Theorie der Transformationsgruppen
Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
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E.
Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
- 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: Generalized Functions (multi-volume series) Target entity description: Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
-
A.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
B.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
C.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
-
D.
Theorie der Transformationsgruppen
Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
-
E.
Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book series
ⓘ
scholarly monograph ⓘ |
| aim |
to present applications of generalized functions to differential equations
ⓘ
to present applications of generalized functions to mathematical physics ⓘ to systematically develop the theory of generalized functions ⓘ |
| audience |
graduate students in mathematics
ⓘ
researchers in functional analysis ⓘ researchers in partial differential equations ⓘ theoretical physicists ⓘ |
| contribution |
systematic exposition of generalized function theory
ⓘ
unified treatment of distributions and their applications ⓘ |
| describedAs | foundational multi-volume work in functional analysis and distribution theory ⓘ |
| field |
distribution theory
ⓘ
functional analysis ⓘ mathematical physics ⓘ partial differential equations ⓘ |
| hasPart |
Generalized Functions (multi-volume series)
self-linksurface differs
ⓘ
surface form:
volume on Fourier transform and convolution of generalized functions
volume on applications to mathematical physics ⓘ volume on basic properties of generalized functions ⓘ volume on elliptic equations and boundary value problems ⓘ |
| influenced |
applications of functional analysis in physics
ⓘ
modern treatments of distribution theory ⓘ research in partial differential equations ⓘ |
| structure | multi-volume ⓘ |
| topic |
Fourier transform of distributions
ⓘ
Green’s functions ⓘ applications to mathematical physics ⓘ boundary value problems ⓘ convolution of distributions ⓘ distributions ⓘ fundamental solutions of differential operators ⓘ Generalized Functions (multi-volume series) self-linksurface differs ⓘ
surface form:
generalized functions
integral transforms ⓘ linear partial differential equations ⓘ operational calculus ⓘ tempered distributions ⓘ |
| usedFor |
modeling singular phenomena in mathematical physics
ⓘ
solving differential equations in generalized function spaces ⓘ study of distribution theory ⓘ |
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: Generalized Functions (multi-volume series) Description of subject: Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Théorie des distributions
Produits tensoriels topologiques et espaces nucléaires
→
relatedWork
→
Generalized Functions (multi-volume series)
ⓘ
this entity surface form:
Théorie des distributions
Generalized Functions (multi-volume series)
→
topic
→
Generalized Functions (multi-volume series)
self-linksurface differs
ⓘ
this entity surface form:
generalized functions
Generalized Functions (multi-volume series)
→
hasPart
→
Generalized Functions (multi-volume series)
self-linksurface differs
ⓘ
this entity surface form:
volume on Fourier transform and convolution of generalized functions