Microlocal Discretization of Singular Integral Operators on Weighted Wiener Amalgam Spaces for the Blind Deconvolution of Relativistic Doppler-Drifting Signals in Alpha-Stable Noise Regimes

Mathematical Applications of Science Fiction We present a rigorous operator-theoretic framework for the blind deconvolution of signals subjected torelativistic Doppler drift, modeled within the phase space of the Lorentz group SO(1, 1), and corrupted bynon-Gaussian α-stable noise processes (0 < α < 2). By constructing a weighted Wiener Amalgam spaceW (Lp, Lq )v adapted to the hyperbolic geometry of the drift, we establish the boundedness of a class ofSingular Integral Operators (SIOs) representing the inverse scattering transformation. We introduce amicrolocal discretization scheme utilizing symplectically deformed Gabor frames, proving that the sparsityof the representation is preserved under relativistic transformations. The central result is a convergencetheorem for an iterative deconvolution algorithm based on the minimization of a fractional lower-ordermoment functional, circumventing the divergence of second-order statistics inherent to the Lévy flight noisemodel. This work bridges the gap between harmonic analysis on locally compact groups and statistical signalprocessing in high-energy astrophysical environments.