Korean Journal of Mathematics

  • 제24권4호
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  • Pages.693-722
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  • 2016
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS

  • 투고 : 2016.06.30
  • 심사 : 2016.12.16
  • 발행 : 2016.12.30
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초록

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.

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참고문헌

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