Multi-box splines

Timothy Goodman

doi:10.1007/s00365-006-0654-3

Multi-box splines

Timothy Goodman

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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
Pages (from-to)	279-301
Number of pages	23
Journal	Constructive Approximation
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s00365-006-0654-3
Publication status	Published - 2007

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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.",

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N2 - 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.

AB - 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.

U2 - 10.1007/s00365-006-0654-3

DO - 10.1007/s00365-006-0654-3

M3 - Article

SN - 0176-4276

VL - 25

SP - 279

EP - 301

JO - Constructive Approximation

JF - Constructive Approximation

IS - 3

ER -

Multi-box splines

Abstract

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