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: Poisson kernel is positive and integrates to 1 | Statement: [Poisson integral, assumption, Poisson kernel is positive and integrates to 1]

Target entity: Poisson kernel is positive and integrates to 1
Context triple: [Poisson integral, assumption, Poisson kernel is positive and integrates to 1]

• A. Poisson kernel chosen
  The Poisson kernel is a fundamental function in harmonic analysis and potential theory used to represent harmonic functions inside a domain from their boundary values, especially in the unit disk and upper half-plane.
• B. Poisson integral
  The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
• C. Fejér kernel
  The Fejér kernel is a sequence of nonnegative trigonometric polynomials used in Fourier analysis to study and ensure the Cesàro (Fejér) summability of Fourier series.
• D. Nevanlinna–Pick kernels
  Nevanlinna–Pick kernels are special positive-definite kernels that characterize when and how analytic interpolation problems of Nevanlinna–Pick type admit solutions, often serving as the reproducing kernels of associated Hilbert spaces of analytic functions.
• E. Koebe quarter theorem
  The Koebe quarter theorem is a fundamental result in complex analysis stating that any univalent holomorphic function on the unit disk maps it onto a domain containing a disk of radius one quarter, providing a sharp bound on the size of the image.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.