Ruijsenaars spectral transform

2024/11/29 by N. Belousov, Belousov, N., S. Khoroshkin +1 · 1 citation
Computer Science · Engineering · #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Image Processing and 3D Reconstruction #Mathematical Physics (math-ph) #Physics and Engineering Research Articles

paper · pdf · doi:10.48550/arxiv.2411.19659

openalex publication_date 2024/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spectral decomposition with respect to the wave functions of Ruijsenaars hyperbolic system defines an integral transform, which generalizes classical Fourier integral. For a certain class of analytical symmetric functions we prove inversion formula and orthogonality relations, valid for complex valued parameters of the system. Besides, we study four regimes of unitarity, when this transform defines isomorphisms of the corresponding L₂ spaces.

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• Complex rational Ruijsenaars model. The two-particle case

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