Abel transform

Target entity: Abel transform
Context triple: [Abel summation, relatedConcept, Abel transform]

• A. Hilbert transform
  The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
• B. Bailey transform
  The Bailey transform is a technique in the theory of basic hypergeometric series that relates pairs of sequences (Bailey pairs) and underlies many identities and transformations in q-series and partition theory.
• C. Sommerfeld-Watson transform
  The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
• D. Gabor transform
  The Gabor transform is a time–frequency analysis technique that represents signals using localized sinusoidal functions, enabling detailed examination of how a signal’s frequency content evolves over time.
• E. Radon transform
  The Radon transform is an integral transform that maps a function to its line integrals over hyperplanes, forming the mathematical foundation of computed tomography and various inverse problems in imaging.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Abel transform
Target entity description: The Abel transform is an integral transform used to reconstruct a radially symmetric function from its line-of-sight projections, widely applied in fields such as tomography, plasma diagnostics, and astrophysics.

• A. Hilbert transform
  The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
• B. Bailey transform
  The Bailey transform is a technique in the theory of basic hypergeometric series that relates pairs of sequences (Bailey pairs) and underlies many identities and transformations in q-series and partition theory.
• C. Sommerfeld-Watson transform
  The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
• D. Gabor transform
  The Gabor transform is a time–frequency analysis technique that represents signals using localized sinusoidal functions, enabling detailed examination of how a signal’s frequency content evolves over time.
• E. Radon transform
  The Radon transform is an integral transform that maps a function to its line integrals over hyperplanes, forming the mathematical foundation of computed tomography and various inverse problems in imaging.
• F. None of above. chosen