Paley–Wiener Theorems of Generalized Fourier Transform Associated with a Cherednik Type Operator on the Real Line

Mejjaoli, Hatem

doi:10.1007/s11785-015-0456-9

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Cited by 4 publications

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“…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: 96%

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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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Section: Introductionmentioning

confidence: 96%

“…Next the analogue of this theorem was established and improved for many other integral transforms, for examples (cf. [1,6,14,[16][17][18]23]). The second subject concerning spectral theorems is the study of tempered distributions with spectral gaps.…”

Section: Introductionmentioning

confidence: 99%