Localized Polynomial Frames on the Interval with Jacobi Weights

  title={Localized Polynomial Frames on the Interval with Jacobi Weights},
  author={Pencho Petrushev and Yuan Xu},
As is well known the kernel of the orthogonal projector onto the polynomials of degree n in L2(wα,β , [−1, 1]) with wα,β(t) = (1−t) (1+t) can be written in terms of Jacobi polynomials. It is shown that if the coefficients in this kernel are smoothed out by sampling a C∞ function then the resulting function has nearly exponential (faster than any polynomial) rate of decay away from the main diagonal. This result is used for the construction of tight polynomial frames for L2(wα,β) with elements… CONTINUE READING

From This Paper

Topics from this paper.


Publications referenced by this paper.

Littlewood-Paley theory and the study of function spaces

  • M. Frazier, B. Jawerth, G. Weiss
  • CBMS No 79
  • 1991
Highly Influential
4 Excerpts

Special functions

  • G. E. Andrews, R. Askey, R. Roy
  • Encyclopedia of Mathematics and its Applications…
  • 1999
1 Excerpt

Ondelletes et OpérateursI: Ondelletes

  • Y. Meyers
  • Hermann, Paris
  • 1990
1 Excerpt

II . An analytic proof of the product formula

  • T. Koornwinder, Jacobi polynomials.
  • SIAM J . Math . Anal .
  • 1975

Orthogonal Polynomials

  • G. Szegő
  • Amer. Math. Soc. Colloq. Publ. Vol.23, Providence…
  • 1975
1 Excerpt

Formulas of the Dirichlet-Mehler type

  • G. Gasper
  • Fractional calculus and its applications
  • 1974
1 Excerpt

Higher Transcendental Functions

  • A. Erdélyi, W. Magnus, F. Oberhettinger, F. G. Tricomi
  • Vol. II, McGraw-Hill, New York
  • 1953

Similar Papers

Loading similar papers…