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: Schauder decomposition | Statement: [Schauder basis, relatedTo, Schauder decomposition]

Target entity: Schauder decomposition
Context triple: [Schauder basis, relatedTo, Schauder decomposition]

• A. Schauder basis chosen
  A Schauder basis is a sequence in a Banach space such that every element of the space can be uniquely represented as a convergent infinite linear combination of the sequence’s vectors.
• B. Riesz basis
  A Riesz basis is a sequence in a Hilbert space that is complete and behaves like an orthonormal basis up to a bounded, invertible linear transformation, allowing stable and unique expansions of vectors.
• C. Neumann series
  The Neumann series is an infinite series expansion used to represent the inverse of an operator or solve integral and differential equations, analogous to a geometric series in functional analysis.
• D. Parseval identity for orthonormal systems in L^2
  The Parseval identity for orthonormal systems in \(L^2\) is a fundamental result in functional analysis stating that the squared norm of a function equals the sum of the squares of its Fourier (or orthonormal expansion) coefficients, expressing energy conservation between a function and its orthonormal series representation.
• E. Lévy–Itô decomposition
  The Lévy–Itô decomposition is a fundamental result in probability theory that expresses any Lévy process as the sum of a Brownian motion with drift and a jump process constructed from a Poisson random measure.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.