On polynomial symbols for subdivision schemes |
| |
Authors: | Morten Nielsen |
| |
Affiliation: | (1) Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg East, Denmark |
| |
Abstract: | Given a dilation matrix A :ℤd→ℤd, and G a complete set of coset representatives of 2π(A
−Tℤd/ℤd), we consider polynomial solutions M to the equation ∑
g∈G
M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric
polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices,
we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of
arbitrary order.
Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network. |
| |
Keywords: | interpolating refinable function polynomial symbols subdivision scheme multiwavelets |
本文献已被 SpringerLink 等数据库收录! |
|