Cardinal series interpolation to nonuniform grids (Q1321513)

Let \(G\) denote the usual orthogonal grid in \(\mathbb{R}^ d\) with spacing \(h\), that is \(G = (h\mathbb{Z})^ d = \{mh:m \in \mathbb{Z}^ d\}\), where \(\mathbb{Z}\) is the set of integers. The paper deals with cardinal series interpolation from \(G\) to a second grid \(\overline G\) defined as the image of \(G\) under a mapping \(\varphi\) from \(\mathbb{R}^ d\) to \(\mathbb{R}^ d\). Cardinal series interpolation is a limiting case of cardinal spline interpolation and is also a limit for interpolation by finite Fourier series as the extent of the grid increases. The main result is a characterization of the boundedness of this interpolation operator in terms of the so-called clustering constraint. Furthermore, an error estimate showing the spectral accuracy of the cardinal series interpolation is presented.