Localized Polynomial Frames on the Ball

@inproceedings{Petrushev2008LocalizedPF,
  title={Localized Polynomial Frames on the Ball},
  author={Pencho Petrushev and Yuan Xu},
  year={2008}
}
Almost exponentially localized polynomial kernels are constructed on the unit ball Bd in Rd with weights Wμ(x) = (1 − |x|2)μ−1/2, μ ≥ 0, by smoothing out the coefficients of the corresponding orthogonal projectors. These kernels are utilized to the design of cubature formulae on Bd with respect to Wμ(x) and to the construction of polynomial tight frames in L2(Bd, Wμ) (called needlets) whose elements have nearly exponential localization. 

References

Publications referenced by this paper.
SHOWING 1-10 OF 18 REFERENCES

Weighted approximation of functions on the unit sphere

  • Yuan Xu
  • Const. Approx
  • 2005
1 Excerpt

Metrics associated to multivariate polynomial inequalities

  • L. Bos, N. Levenberg, S. Waldron
  • Advances in Constructive Approximation…
  • 2004
2 Excerpts

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