Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

Oscillating multipliers on the Heisenberg group

E. K. NarayananS. Thangavelu — 2001

Colloquium Mathematicae

Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator - 1 / 2 s i n is bounded on L p ( H ) for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on L p in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.

A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on n

EK. NarayananS. Thangavelu — 2006

Annales de l’institut Fourier

We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on n . 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 n if and only if f × μ r ( z ) = 0 for r &gt; B + | z | for all z n . This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When n = 1 we show that the two conditions f × μ r ( z ) = μ r × f ( z ) = 0 for r &gt; B + | z | imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter...

Page 1

Download Results (CSV)