Bulletin of the
Korean Mathematical Society BKMS

For an entire function $f$ whose Fourier transform has a compact support confined to $[-\pi,\pi]$ and restriction to $\mathbb R$ belongs to $L^2(\mathbb R)$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points $\lambda_n\in\mathbb R, n \in \mathbb{Z},$ under the condition that $$ \limsup_{n\to \infty} |\lambda_n - n |< \frac{1}{4}. $$

Keywords: Riesz basis, frame, nonuniform sampling, nonharmonic Fourier series

MSC numbers: 94A20