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Completeness of systems of complex exponentials and the Lambert $ W$ functions

Author(s): André Boivin; Hualiang Zhong
Journal: Trans. Amer. Math. Soc. 359 (2007), 1829-1849.
MSC (2000): Primary 42C15, 42C30, 34K07; Secondary 30B50
Posted: November 22, 2006
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Abstract: We study some of the properties of the solution system $ \{e^{i\lambda_nt}\}$ of the delay-differential equation $ y'(t) = ay(t-1)$. We first establish some general results on the stability of the completeness of exponential systems in $ L^2$ and then show that the solution system above is always complete, but is not an unconditional basis in $ L^2(-1/2,1/2)$.

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Additional Information:

André Boivin
Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
Email: boivin@uwo.ca

Hualiang Zhong
Affiliation: Robarts Research Institute, 100 Perth Drive, P.O. Box 5015, London, Ontario, Canada N6A 5K8
Address at time of publication: Department of Radiation Oncology, Virginia Commonwealth University, 401 College Street, Richmond, Virginia 23298
Email: hzhong@vcu.edu

DOI: 10.1090/S0002-9947-06-03950-X
PII: S 0002-9947(06)03950-X
Received by editor(s): July 4, 2003
Received by editor(s) in revised form: February 4, 2005
Posted: November 22, 2006
Additional Notes: The first author was partially supported by a grant from NSERC of Canada
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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