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We provide a new estimator of integral operators with smooth kernels,obtained from a set of scattered and noisy impulse responses. The proposedapproach relies on the formalism of smoothing in reproducing kernel Hilbertspaces and on the choice of an appropriate regularization term that takes thesmoothness of the operator into account. It is numerically tractable in verylarge dimensions. We study the estimator's robustness to noise and analyze itsapproximation properties with respect to the size and the geometry of thedataset. In addition, we show minimax optimality of the proposed estimator.

Estimation of linear operators from scattered impulse responses