It is known that multiresolution analysis (MRA) of L2(ℝ d) can be made by using polyharmonic spline functions. These are tempered distributions which are annihilated by the iterate of the Laplacian operator in the complement of a discrete set and which admit continuous derivatives up to some order r. Here we prove that the admissible derivatives of the cardinal Lagrangian polyharmonic spline have exponential decay, deducing the r-regularity of the MRA for any acceptable dilation matrix
Bacchelli, B. (2010). Some notes on MRA with Polyharmonic Splines. In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III (pp.516-519). American Institute of Physics [10.1063/1.3498525].
Some notes on MRA with Polyharmonic Splines
Bacchelli, B
2010
Abstract
It is known that multiresolution analysis (MRA) of L2(ℝ d) can be made by using polyharmonic spline functions. These are tempered distributions which are annihilated by the iterate of the Laplacian operator in the complement of a discrete set and which admit continuous derivatives up to some order r. Here we prove that the admissible derivatives of the cardinal Lagrangian polyharmonic spline have exponential decay, deducing the r-regularity of the MRA for any acceptable dilation matrix
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