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: Schwartz space S(ℝⁿ) ⊂ L²(ℝⁿ) ⊂ S′(ℝⁿ) | Statement: [Gelfand triple, example, Schwartz space S(ℝⁿ) ⊂ L²(ℝⁿ) ⊂ S′(ℝⁿ)]

Target entity: Schwartz space S(ℝⁿ) ⊂ L²(ℝⁿ) ⊂ S′(ℝⁿ)
Context triple: [Gelfand triple, example, Schwartz space S(ℝⁿ) ⊂ L²(ℝⁿ) ⊂ S′(ℝⁿ)]

• A. Schwartz space chosen
  Schwartz space is the function space of rapidly decreasing smooth functions on Euclidean space, fundamental in distribution theory and Fourier analysis.
• B. Schwartz–Bruhat space
  The Schwartz–Bruhat space is a function space of rapidly decreasing smooth (or locally constant with compact support, in the non-Archimedean case) test functions on a locally compact abelian group, fundamental in harmonic analysis and number theory.
• C. Lebesgue spaces
  Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
• D. Gelfand triples (rigged Hilbert spaces)
  Gelfand triples (rigged Hilbert spaces) are a mathematical framework that extends Hilbert spaces to rigorously handle generalized eigenvectors and distributions, particularly in quantum mechanics and functional analysis.
• E. Montel space
  A Montel space is a type of locally convex topological vector space in which every closed and bounded set is compact, implying strong convergence and compactness properties useful in functional analysis and distribution theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.