Functional Analysis: Introduction to Further Topics in Analysis
E542635
"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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Functional Analysis: Introduction to Further Topics in Analysis canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T5709653 — 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: Functional Analysis: Introduction to Further Topics in Analysis Context triple: [Elias Stein, notableWork, Functional Analysis: Introduction to Further Topics in Analysis]
-
A.
"Functional Analysis"
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
-
B.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
C.
Applied Functional Analysis
Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
-
D.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
E.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
- 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: Functional Analysis: Introduction to Further Topics in Analysis Target entity description: "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.
-
A.
"Functional Analysis"
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
-
B.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
C.
Applied Functional Analysis
Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
-
D.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
E.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
textbook ⓘ |
| author |
Elias M. Stein
ⓘ
linked to:
Elias Stein
Rami Shakarchi ⓘ |
| countryOfPublication |
United States
ⓘ
linked to:
United States of America
|
| field |
functional analysis
ⓘ
harmonic analysis ⓘ operator theory ⓘ partial differential equations ⓘ |
| format |
ebook
ⓘ
hardcover ⓘ |
| hasApplicationArea |
harmonic analysis
ⓘ
operator theory ⓘ partial differential equations ⓘ |
| hasVolumeInSeries |
Complex Analysis
ⓘ
Fourier Analysis: An Introduction ⓘ Real Analysis: Measure Theory, Integration, and Hilbert Spaces ⓘ |
| intendedUse |
course textbook
ⓘ
self-study reference ⓘ |
| language | English ⓘ |
| level | advanced graduate ⓘ |
| partOfSeries | Princeton Lectures in Analysis ⓘ |
| prequel |
Complex Analysis
ⓘ
Fourier Analysis: An Introduction ⓘ Real Analysis: Measure Theory, Integration, and Hilbert Spaces ⓘ |
| publicationYear | 2011 ⓘ |
| publisher | Princeton University Press ⓘ |
| seriesNumber | 4 ⓘ |
| subjectArea |
analysis
ⓘ
pure mathematics ⓘ |
| targetAudience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| topic |
Banach spaces
ⓘ
Fourier analysis ⓘ Hilbert spaces ⓘ Sobolev spaces ⓘ applications to partial differential equations ⓘ bounded linear operators ⓘ compact operators ⓘ distributions ⓘ semigroups of operators ⓘ spectral theory ⓘ unbounded operators ⓘ |
| usesPrerequisites |
Hilbert space theory
ⓘ
basic functional analysis ⓘ measure 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: Functional Analysis: Introduction to Further Topics in Analysis Description of subject: "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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.