On the excess of complex exponential systems in L2(−a, a)

In this article we give new criteria for two complex sequences to have the same excess in the sense of Paley and Wiener in L2(−a, a). As a result, we prove that given any positive integer q, a real number α ∈ (0, 1/(2π)), and complex numbers ν0 = 0, νn = nq + iα log |nq|, |n| 1, the exponential system {tkeitνn : k = 0, 1, . . . , q −1}∞n=−∞ has excess 0 in L2(−π,π).  2004 Elsevier Inc. All rights reserved