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: Plancherel theorem | Statement: [Fourier inversion theorem, isRelatedTo, Plancherel theorem]

Target entity: Plancherel theorem
Context triple: [Fourier inversion theorem, isRelatedTo, Plancherel theorem]

• A. Plancherel theorem for locally compact abelian groups chosen
  The Plancherel theorem for locally compact abelian groups is a fundamental result in harmonic analysis that identifies the Fourier transform as a unitary isomorphism between an L²-space on the group and an L²-space on its dual group, preserving inner products and norms.
• B. Parseval's theorem
  Parseval's theorem is a fundamental result in Fourier analysis that equates the total energy of a function in the time (or spatial) domain with the total energy of its representation in the frequency domain.
• C. Plancherel measure
  The Plancherel measure is a canonical measure on the unitary dual of a group that describes how the regular representation decomposes into irreducible unitary representations in harmonic analysis.
• D. Fourier inversion theorem
  The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
• E. Riesz–Fischer theorem
  The Riesz–Fischer theorem is a fundamental result in functional analysis that establishes the equivalence between square-summable sequences and square-integrable functions, providing the foundation for the Hilbert space structure of L² spaces.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.