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: Wiener’s Tauberian theorem | Statement: [Tauberian theorems, relatedConcept, Wiener’s Tauberian theorem]

Target entity: Wiener’s Tauberian theorem
Context triple: [Tauberian theorems, relatedConcept, Wiener’s Tauberian theorem]

• A. Tauberian theorems
  Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
• B. Paley–Wiener theorem
  The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
• C. Herglotz's theorem
  Herglotz's theorem is a fundamental result in harmonic analysis and probability theory that characterizes positive-definite functions on the unit circle via representing measures.
• D. 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.
• E. Dunford–Schwartz theorem
  The Dunford–Schwartz theorem is a fundamental result in functional analysis and ergodic theory that provides convergence properties for iterates of certain linear operators on L¹ and L^∞ spaces.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Wiener’s Tauberian theorem
Target entity description: Wiener’s Tauberian theorem is a fundamental result in harmonic analysis that characterizes when the translates of a function on the real line span a dense subspace of certain function spaces, with key applications to summability methods and Fourier analysis.

• A. Tauberian theorems chosen
  Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
• B. Paley–Wiener theorem
  The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
• C. Herglotz's theorem
  Herglotz's theorem is a fundamental result in harmonic analysis and probability theory that characterizes positive-definite functions on the unit circle via representing measures.
• D. 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.
• E. Dunford–Schwartz theorem
  The Dunford–Schwartz theorem is a fundamental result in functional analysis and ergodic theory that provides convergence properties for iterates of certain linear operators on L¹ and L^∞ spaces.
• F. None of above.