A Property of Infinitely Differentiable Functions

Bang, Ha Huy

doi:10.2307/2047695

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Cited by 31 publications

(47 citation statements)

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“…Here we investigate the support of a function only in terms of its Mellin (or inverse Mellin) transform without passing to the complexification. Similar "real variable" results have been obtained for the Fourier transform [1,2,7,8] , the Hankel transform [10], the Y-transform [9], and the Airy transform [11].…”

Section: Introductionsupporting

confidence: 72%

New type Paley-Wiener theorems for the modified multidimensional Mellin transform

Tuan

1998

The Journal of Fourier Analysis and Applications

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Section: Introductionsupporting

confidence: 72%

New type Paley-Wiener theorems for the modified multidimensional Mellin transform

Tuan

1998

The Journal of Fourier Analysis and Applications

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“…The fundamental theorem given by Bang (cf. [4]) can be stated as follows. Let f be a C ∞ -function on R such that for all n ∈ N, the function …”

Section: Introductionmentioning

confidence: 99%

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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“…Specialising to bi-K-invariant functions yields (real) Paley-Wiener theorems for the inverse spherical transform for general noncompact semisimple Lie groups. Our approach is based on real analysis techniques developed by H. H. Bang, see [2] and [3], and V.K. Tuan, see [10].…”

Section: Introductionmentioning

confidence: 99%