• Title/Summary/Keyword: inversion Theorems

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Strong Large Deviations Theorems for the Ratio of the Independent Random Variables

  • Cho, Dae-Hyeon;Jeon, Jong-Woo
    • Journal of the Korean Statistical Society
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    • v.23 no.2
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    • pp.239-250
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    • 1994
  • In this paper, we prove a strong large deviations theorem for the ratio of independent randoem variables with error rate of $O(n^{-1})$. To obtain our results we use the inversion formula for the tail probability and apply the Chaganty and Sethuraman's (1985) approach.

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SOME INTEGRAL TRANSFORMS INVOLVING EXTENDED GENERALIZED GAUSS HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Kachhia, Krunal B.;Prajapati, Jyotindra C.;Purohit, Sunil Dutt
    • Communications of the Korean Mathematical Society
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    • v.31 no.4
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    • pp.779-790
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    • 2016
  • Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.

SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS

  • Mejjaoli, Hatem
    • Korean Journal of Mathematics
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    • v.24 no.4
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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.