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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

Kevin Smith
Kevin Smith*
Affiliation:
Cambridge, United Kingdom (email: k.p.q.smith@gmail.com)

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
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 137 - 139
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