Authors:
Antonio Avantaggiati
;
Paola Loreti
and
Pierluigi Vellucci
Affiliation:
Sapienza Università di Roma, Italy
Keyword(s):
Kadec's 1/4-theorem, Riesz Basis, Exponential Bases, Sinc Bases, Sampling Theorem.
Related
Ontology
Subjects/Areas/Topics:
Informatics in Control, Automation and Robotics
;
Signal Processing, Sensors, Systems Modeling and Control
;
Signal Reconstruction
Abstract:
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 L2(-p,p). In this paper we prove that a/p (where a is the Lamb-
Oseen constant) is a stability bound for the sinc basis on L2(-p,p). The difference between the two values
a/p - 1/4, is ˜ 0.15, therefore the stability bound for the sinc basis on L2(-p,p) is greater than Kadec’s
stability bound (i.e. 1/4).