Monotonicity preserving subdivision schemes (Q2366704)

Starting from some initial values \(\{f_ i^ 0\}\), the binary subdivision scheme \(f^{n+1}_ i = \sum^ \infty_{j=-\infty} a_{i- 2j}f^ n_ j\) produces values \(\{f_ i^{n+1}\}\) (at level \(n+1\)), on the basis of the values \(\{f^ n_ i\}\) assigned to the binary mesh points \(\{2^{-n}i\}^ \infty_{i=-\infty}\). The author studies schemes with a compact support, i.e., with \(a_ i = 0\) for \(i<0\) and \(i>k\), \(k\) is fixed. He proves certain properties (positivity, monotonicity) of the limit function \(f\) and the refinable function \(E(t)\) assuming similar properties of the initial data and the mask \(\{a_ i\}\) of the scheme. A class of schemes is described which have bell-shaped refinable functions.