Abstract
Under a suitable sparsity condition on the exponents Λ=(λk=τk+iσk), it is shown that the individual terms\(c_T = \{ c_k e^{i\lambda _k T} \} \) can be obtained from observation of the L2 function\(f(t) = \sum {c_k e^{i\lambda _k t} } \) through the ‘window’ t∈[0, δ]—with an l2 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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Communicated by Hans G. Feichtinger
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Seidman, T.I., Avdonin, S.A. & Ivanov, S.A. The ‘window problem’ for series of complex exponentials. The Journal of Fourier Analysis and Applications 6, 233–254 (2000). https://doi.org/10.1007/BF02511154
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DOI: https://doi.org/10.1007/BF02511154