منابع مشابه
S Theorem for the Heisenberg Group
If an integrable function f on the Heisenberg group is supported on the set B × R where B ⊂ Cn is compact and the group Fourier transform f̂(λ) is a finite rank operator for all λ ∈ R \ {0}, then f ≡ 0.
متن کاملThe Heisenberg group and Pansu’s Theorem
The goal of these notes is to introduce the reader to the Heisenberg group with its CarnotCarathéodory metric and to Pansu’s differentiation theorem. As they are very similar, we will first study Rademacher’s theorem about Lipschitz maps and then see how the same technique can be applied in the more complex setting of the Heisenberg group.
متن کاملBenedicks’ Theorem for the Heisenberg Group
If an integrable function f on the Heisenberg group is supported on the set B × R where B ⊂ Cn is compact and the group Fourier transform f̂(λ) is a finite rank operator for all λ ∈ R \ {0}, then f ≡ 0.
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— We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on Cn. If f(z)e 1 4 |z| 2 is a Schwartz class function we show that f is supported in a ball of radius B in Cn if and only if f×μr(z) = 0 for r > B+ |z| for all z ∈ Cn. This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When n = 1 w...
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The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover , the Hardy-Littlewood-Sobolev inequality is established.
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2009
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2437