Efficient Numerical Computation of Spiral Spectra with Exponentially-Weighted Preconditioners

The paper proves uniform weighted resolvent bounds and unweighted exponential growth/ boundedness criteria for spiral waves on large disks via radial spatial dynamics, exponential dichotomies, and a far-field/boundary-layer gluing argument. The candidate solution follows the same structure: reduction to a first-order r-flow, choice of η ∈ J0(λ) to create a dichotomy, robustness under tail perturbations, and a core–tail matching map to obtain uniform bounds away from Σ∞, plus a boundary-layer pseudomode argument when 0 ∉ J0(λ*). Minor mismatches are present (e.g., the size/decay of the tail perturbation and the exact function space), but they do not alter the logic or conclusions. Overall, the model’s solution is a faithful proof sketch of Theorems 3.8 and 3.9.