### Abstract

We construct local generators, comprising r functions, for refinable spaces of bivariate Cn-1 spline functions of degree n on meshes comprising all lines through points of the integer lattice in the directions of n + r + 1 pairwise linearly independent vectors with integer components. The generators are characterised by their Fourier transforms. Their shifts are shown to form a Riesz basis if and only if at most r lines in the mesh intersect other than in the integer lattice, which can occur for n = 2r - 1. The symmetry of these generators is studied and examples are given.

Original language | English |
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Pages (from-to) | 279-301 |

Number of pages | 23 |

Journal | Constructive Approximation |

Volume | 25 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 |

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## Cite this

Goodman, T. (2007). Multi-box splines.

*Constructive Approximation*,*25*(3), 279-301. https://doi.org/10.1007/s00365-006-0654-3