3 problems

Let $V(\phi)$ be a shift-invariant space, let $k$ and $\nu$ be positive integers, and let $\\{x_i:i\in\mathbb{Z}\\}$ be a separated set. For a function $f$, consider the nonuniform…

Let $Q_m$ denote the spline generator and let $V(Q_m)$ be the shift-invariant spline space it generates. A sequence $\\{x_i:i\in\mathbb{Z}\\}$ is separated if its distinct points h…

Let $d$ be the dimension, and consider the pointwise Fourier-decay result asserting that for some generator $\widehat{\phi}_{i_0}$, the quantity…