Katz–Radon Transform of ℓ-Adic Representations

We prove a simple explicit formula for the local Katz–Radon transform of an ℓ-adic representation of the Galois group of the fraction field of a strictly henselian discrete valuation ring with positive residual characteristic, which can be defined as the local additive convolution with a fixed tame character. The formula is similar to the one proved by Arinkin in the $\mathcal D$-module setting, and answers a question posed by Katz.