TL;DR
The paper introduces the Joint-Eigenspace Fourier Transform (JEFT), a new Fourier transform on noncompact symmetric spaces, extending classical transforms like Helgason's and Harish-Chandra's, with potential applications in harmonic analysis.
Contribution
It presents the JEFT as a novel Fourier transform model on noncompact symmetric spaces, generalizing existing transforms such as Helgason's and Harish-Chandra's.
Findings
Defines the JEFT on noncompact symmetric spaces.
Shows JEFT as a Poisson-completion of Helgason's transform.
Connects JEFT to classical Fourier analysis on Lie groups.
Abstract
The JEFT is the acronym for the Joint-Eigenspace Fourier Transform defined on a noncompact symmetric space. It is a consequence of a general construction of a Fourier transform modelled on the Harish-Chandra Fourier transform (on a semi-simple Lie group with finite centre) which (on the corresponding symmetric space of the noncompact type) serves as the Poisson-completion of the famous Helgason Fourier transform
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Taxonomy
TopicsAdvances in Oncology and Radiotherapy