Prove genuinely nonexponential wedge-corrector decay for specified exponentially localized data

Establish that a specified exponentially localized source and incoming-ray data for the conservative kinetic wedge problem force a genuinely nonexponential wedge corrector by deriving the far-field asymptotics of the restricted collision resolvent and proving nonvanishing of its leading coefficient.

Background

The paper proves algebraic decay of the bounded wedge corrector at every rate below the first positive Dirichlet exponent, even when the source and incoming data are assumed to decay algebraically. It explains that the conservative collision operator has no spectral gap and that its low-frequency behavior is diffusive, suggesting algebraic rather than exponential far-field behavior.

However, the paper does not establish a sharp lower bound or a full far-field asymptotic for any specified exponentially localized datum. Such a result would require asymptotic analysis of the restricted resolvent and verification that the coefficient of the leading decaying harmonic mode is nonzero; this would show that the algebraic decay is genuinely forced rather than merely an artifact of the upper-bound method.