Explicit bounds of complex exponential frames on a complex field

  • P. VellucciEmail author


In the context of Riesz basis, studies on classical system of exponentials find their origin in the celebrated 1934’s work of Paley and Wiener. The stability question of exponential frames was considered in 1952 by Duffin and Schaeffer in their seminal paper. This article discusses the stability of complex exponential frames \({\left\{e^{{i\lambda}_{n}t}\right\}_{n\in\mathbb{Z}}}\) in \({L^{2}(-\pi,\pi)}\) and presents explicit upper and lower bounds for general complex exponential frames perturbed along the entire complex plane.

Key words and phrases

Kadec’s 1/4-theorem Riesz basis frames exponential bases 

Mathematics Subject Classification

42C05 42C15 42C30 


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The author thanks Prof. Laura De Carli for stimulating discussions concerning this work and the anonymous referee for some useful comments.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of Roma TRERomeItaly

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