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.

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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
foundations of real analysis
linked to: Cours d’Analyse
countryOfOrigin Germany
field Fourier analysis
mathematics
real analysis
hasTitleTranslation 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 series
linked to: Fourier analysis

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
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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Bernhard Riemann notableWork Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe hasTitleTranslation On the Representability of a Function by a Trigonometric Series
linked to: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe originalTitle Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe