• 제목/요약/키워드: real Paley-Wiener theorem

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REAL VERSION OF PALEY-WIENER-SCHWARTZ THEOREM FOR ULTRADISTRIBUTIONS WITH ULTRADIFFERENTIABLE SINGULAR SUPPORT

  • Cho, Jong-Gyu;Kim, Kwang-Whoi
    • 대한수학회보
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    • 제36권3호
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    • pp.483-493
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    • 1999
  • We extend the Paley-Wiener-Schwartz theorem to the space of ultradistributions with respect to ultradifferentiable singular support and obtain its real version. That is, we obtain the growth condition in some tubular neighborhood of n of the Fourier transform of ultradistributions of Roumieu (or Beurling) type with ultradifferentiable singular support contained in a ball centered at the origin, and its real version.

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SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS

  • Mejjaoli, Hatem
    • Korean Journal of Mathematics
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    • 제24권4호
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    • pp.693-722
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    • 2016
  • In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.