Norm dependence of the coefficient map on the window size.

For sparse exponent sequences (λk) ∞ −∞, satisfying a suitable ‘separation condition’ defined by an auxiliary sequence ψ, one has a ‘coefficient map’ Cδ giving (ck) ∞ −∞ =: c from observation of f = ∑∞ k=−∞ ck e iλkt on any arbitrarily small interval [−δ, δ]. In terms of ψ, we estimate the norm of Cδ : L [−δ, δ] → `, asymptotically as δ → 0. In particular, for (λk) ∞ −∞ ∼ k (p > 1) we get a bound which is exponential in (1/δ)1/(p−1), generalizing an earlier result for the case p = 2.