Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
E47354
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
All labels observed (2)
How this entity was disambiguated
This entity first appeared as the object of triple T373791 — 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.
Target entity: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe Context triple: [Bernhard Riemann, notableWork, Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe]
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A.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
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B.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
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C.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
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D.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
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E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe Target entity description: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
A.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
B.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
C.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
-
D.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical paper
ⓘ
scientific article ⓘ |
| author | Bernhard Riemann ⓘ |
| authorBirthYear | 1826 ⓘ |
| authorDeathYear | 1866 ⓘ |
| authorNationality | German ⓘ |
| concerns |
behavior of Fourier coefficients
ⓘ
conditions for function representation ⓘ integrability of functions ⓘ |
| contributedTo |
development of modern integration theory
ⓘ
Cours d’Analyse ⓘ
surface form:
foundations of real analysis
|
| countryOfOrigin | Germany ⓘ |
| field |
Fourier analysis
ⓘ
mathematics ⓘ real analysis ⓘ |
| hasTitleTranslation |
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
self-linksurface differs
ⓘ
surface form:
On the Representability of a Function by a Trigonometric Series
|
| historicalPeriod | 19th-century mathematics ⓘ |
| impact |
advanced rigorous treatment of trigonometric series
ⓘ
shaped modern understanding of integration ⓘ |
| influenced |
Georg Cantor
ⓘ
Henri Lebesgue ⓘ development of measure theory ⓘ rigorous theory of Fourier series ⓘ |
| introducedConcept | Riemann integral ⓘ |
| language | German ⓘ |
| mainTopic |
Fourier analysis
ⓘ
surface form:
Fourier series
Riemann integral ⓘ conditions for Fourier series convergence ⓘ convergence of trigonometric series ⓘ representation of functions by trigonometric series ⓘ |
| mathematicalSubjectClassification |
Fourier analysis
ⓘ
real functions ⓘ |
| originalTitle | Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe self-link ⓘ |
| publicationYear | 1854 ⓘ |
| relatedConcept |
Dirichlet conditions
ⓘ
Riemann sums ⓘ piecewise continuity ⓘ pointwise convergence ⓘ uniform convergence ⓘ |
| relatedTo |
Fourier series representation of periodic functions
ⓘ
history of Fourier analysis ⓘ history of real analysis ⓘ |
| status | seminal work in analysis ⓘ |
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Subject: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe Description of subject: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.