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 {-π,π). In this paper we prove that α/π (where α is the Lamb-Oseen constant) is a stability bound for the sine basis on L2(-π,π). The difference between the two values α/π-1/4, is ≈ 0.15, therefore the stability bound for the sinc basis on L2(-π,π) is greater than Kadec's stability bound (i.e. 1/4).

An Explicit Bound for Stability of Sinc Bases / Avantaggiati, Antonio; Loreti, Paola; Vellucci, Pierluigi. - STAMPA. - 1:(2015), pp. 473-480. (Intervento presentato al convegno 12th International Conference on Informatics in Control, Automation and Robotics tenutosi a Colmar, Alsace, France nel 21-23 July, 2015) [10.5220/0005512704730480].

### An Explicit Bound for Stability of Sinc Bases

#### 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 {-π,π). In this paper we prove that α/π (where α is the Lamb-Oseen constant) is a stability bound for the sine basis on L2(-π,π). The difference between the two values α/π-1/4, is ≈ 0.15, therefore the stability bound for the sinc basis on L2(-π,π) is greater than Kadec's stability bound (i.e. 1/4).
##### Scheda breve Scheda completa
2015
12th International Conference on Informatics in Control, Automation and Robotics
Kadec’s 1/4-theorem, Riesz Basis, Exponential Bases, Sinc Bases, Sampling Theorem.
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
An Explicit Bound for Stability of Sinc Bases / Avantaggiati, Antonio; Loreti, Paola; Vellucci, Pierluigi. - STAMPA. - 1:(2015), pp. 473-480. (Intervento presentato al convegno 12th International Conference on Informatics in Control, Automation and Robotics tenutosi a Colmar, Alsace, France nel 21-23 July, 2015) [10.5220/0005512704730480].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/849055`