An explicit bound for stability of sinc bases

摘要

It is well known that exponential Riesz bases are stable. The celebrated theorem by Kadec shows that 1/4 is a stability bound for the exponential basis on L(−π;π). In this paper we prove that α/π (where α is the Lamb-Oseen constant) is a stability bound for the sinc basis on L(−π;π). The difference between the two values α/π−1/4, is ≈ 0.15, therefore the stability bound for the sinc basis on L(−π;π) is greater than Kadec's stability bound (i.e. 1/4).