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On the completeness of sets of complex exponentials
Part of:
Harmonic analysis in one variable
Published online by Cambridge University Press: 01 June 2011
Abstract
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The completeness of sets of complex exponentials {eiλf(n)⋅:f∈ℤ} in Lp(−π,π), 1<p≤2, is considered under Levinson’s sufficient condition in the non-trivial case λ≥1−(1/p). All such sets are determined explicitly.
MSC classification
Secondary:
42A65: Completeness of sets of functions
- Type
- Research Article
- Information
- Copyright
- Copyright © London Mathematical Society 2011
References
[1]Levinson, N., ‘On non-harmonic Fourier series’, Ann. of Math. (2) 37 (1936) 919–936.CrossRefGoogle Scholar
[2]Paley, R. E. A. C. and Wiener, N., Fourier transforms in the complex domain (American Mathematical Society, Providence, RI, 1934).Google Scholar
[3]Smith, K., ‘On complete interpolating sequences and sampling expansions’, LMS J. Comput. Math. 13 (2010) 1–9.CrossRefGoogle Scholar
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