The ‘window problem’ for series of complex exponentials
نویسنده
چکیده
Under a suitable sparsity condition on the exponents Λ = {λk = τk+ iσk}, it is shown that the individual terms cT = {ck ek} can be obtained from observation of the L function f(t) = ∑ ck e iλkt through the ‘window’ t ∈ [0, δ] — with an ` estimate (uniform for such Λ) asymptotically as T, δ → 0. Some applications are given to control theory for partial differential equations.
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