Explicit bounds of complex exponential frames on a complex field

Abstract

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.