A sampling theorem by perturbing the zeros of a sine-type function

ABSTRACT

In this paper, we present a generalisation of the classical Shannon sampling theorem that allows for sampling sets that are perturbations of the set of zeros of a sine-type function. Such sampling sets may be non-equidistant and non-periodic.

Keywords:

• Shannon sampling
• Paley–Wiener spaces
• zeros of a sine-type function
• Riesz basis
• non-equidistant sampling

2010 Mathematics Subject Classification:

• 30E05, 30E10

Disclosure statement

No potential conflict of interest was reported by the authors.