Roe's theorem revisited

Andersen, Nils Byrial

doi:10.1080/10652469.2014.976219

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Cited by 6 publications

(2 citation statements)

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“…Theorem 6.3 and Corollary 6.4 are the analogue of the new real Paley-Wiener theorems for the Fourier transform, proved by Andersen (see [2]). …”

Section: Choose and Fixmentioning

confidence: 99%

“…If a function and all its derivatives and integrals are absolutely uniformly bounded, then the function is a sine function with period 2π. This result has been studied and generalized, see [2,13,[15][16][17][18]21] including generalizations to differential and differential-difference operators with constant coefficients in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Spectral Theorems Associated to the Dunkl Operators

Mejjaoli

2016

Korean Journal of Mathematics

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Abstract. 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 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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“…Theorem 6.3 and Corollary 6.4 are the analogue of the new real Paley-Wiener theorems for the Fourier transform, proved by Andersen (see [2]). …”

Section: Choose and Fixmentioning

confidence: 99%