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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 (24)
참고문헌 신청
N.B. Andersen / 2010 / Real Paley-Wiener theorems and local spectral radius formulas / Trans. Amer. Math. Soc 362:3616~3640
N.B. Andersen / 2015 / Roe's theorem revisited / Integral Transf. and Special Functions 26(3):165~172
P.K. Banerji / 2006 / Tempered distributional sine (co-sine) transform / Integral Transforms Spec. Funct 17(11):759~768
H.H. Bang / 1990 / A property of infinitely differentiable functions / Proc. Amer. Math. Soc 108(1):73~76
G. Birkoff / 1965 / A Survey of Modern Algebra / MacMillan
N.B. Andersen / 2015 / Roe's theorem revisited / Integral Transf. and Special Functions 26(3):165~172
P.K. Banerji / 2006 / Tempered distributional sine (co-sine) transform / Integral Transforms Spec. Funct 17(11):759~768
H.H. Bang / 1990 / A property of infinitely differentiable functions / Proc. Amer. Math. Soc 108(1):73~76
G. Birkoff / 1965 / A Survey of Modern Algebra / MacMillan
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