Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Fejér’s theorem on Fourier series | Statement: [Lipót Fejér, knownFor, Fejér’s theorem on Fourier series]

Target entity: Fejér’s theorem on Fourier series
Context triple: [Lipót Fejér, knownFor, Fejér’s theorem on Fourier series]

• A. Dirichlet theorem on Fourier series
  The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
• B. Dini test for convergence of Fourier series
  The Dini test for convergence of Fourier series is a classical criterion in harmonic analysis that gives sufficient conditions, involving the behavior of a function near a point, to ensure the pointwise convergence of its Fourier series there.
• C. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
  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.
• D. Carleson theorem on almost-everywhere convergence
  The Carleson theorem on almost-everywhere convergence is a fundamental result in harmonic analysis stating that the Fourier series of any square-integrable function on the circle converges almost everywhere to the function itself.
• E. Trigonometric Series, Vol. I
  Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Fejér’s theorem on Fourier series
Target entity description: Fejér’s theorem on Fourier series is a fundamental result in harmonic analysis stating that the Cesàro means (Fejér means) of the Fourier series of a continuous periodic function always converge uniformly to the function itself.

• A. Dirichlet theorem on Fourier series
  The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
• B. Dini test for convergence of Fourier series
  The Dini test for convergence of Fourier series is a classical criterion in harmonic analysis that gives sufficient conditions, involving the behavior of a function near a point, to ensure the pointwise convergence of its Fourier series there.
• C. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
  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.
• D. Carleson theorem on almost-everywhere convergence
  The Carleson theorem on almost-everywhere convergence is a fundamental result in harmonic analysis stating that the Fourier series of any square-integrable function on the circle converges almost everywhere to the function itself.
• E. Trigonometric Series, Vol. I
  Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
• F. None of above. chosen