The ‘window problem’ for series of complex exponentials

Under a suitable sparsity condition on the exponents Λ=(λk=τk+iσk), it is shown that the individual terms can be obtained from observation of the L2 function 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...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2000-01, Vol.6 (3), p.233-254
Main Authors: Seidman, T. I., Avdonin, S. A., Ivanov, S. A.
Format: Article
Language:English
Subjects:
Control theory
Fourier analysis
Partial differential equations
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Summary:Under a suitable sparsity condition on the exponents Λ=(λk=τk+iσk), it is shown that the individual terms can be obtained from observation of the L2 function 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.
ISSN:1069-5869
1531-5851
DOI:10.1007/BF02511154