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3 results

  • THE DECAY OF THE WALSH COEFFICIENTS OF SMOOTH FUNCTIONS

  • Part of
  • JOSEF DICK
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 80 / Issue 3 / December 2009
    Published online by Cambridge University Press:
    02 July 2009, pp. 430-453
    Print publication:
    December 2009
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  • We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and nonperiodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown.

  • GENERALIZED FOURIER EXPANSIONS OF DIFFERENTIABLE FUNCTIONS ON THE SPHERE

  • FRANCISCO JAVIER GONZÁLEZ VIELI
  • Journal:
    Glasgow Mathematical Journal / Volume 47 / Issue 2 / May 2005
    Published online by Cambridge University Press:
    27 July 2005, pp. 339-345
    Print publication:
    May 2005
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  • We show that the Fourier expansion in spherical $h$-harmonics (from Dunkl's theory) of a function $f$ on the sphere converges uniformly to $f$ if this function is sufficiently differentiable.

  • Algebraic Elements and Sets of Uniqueness in the Group of Integers of a p-Series Field

  • Bruce Aubertin
  • Journal:
    Canadian Mathematical Bulletin / Volume 29 / Issue 2 / 01 June 1986
    Published online by Cambridge University Press:
    20 November 2018, pp. 177-184
    Print publication:
    01 June 1986
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  • Let G be the group of integers of a p-series field. A class {E(θ)} of perfect null subsets of G is introduced and classified into M-sets and U-sets according to the arithmetical nature of the field element θ. This is analogous to the well-known classification, involving Pisot numbers, of certain Cantor sets on the circle.