Restriction theorems for the Heisenberg group.
On almost everywhere and mean convergence of Hermite and Laguerre expansions
Some remarks on Bochner-Riesz means
We study norm convergence of Bochner-Riesz means associated with certain non-negative differential operators. When the kernel satisfies a weak estimate for large values of m we prove norm convergence of for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.
On conjugate Poisson integrals and Riesz transforms for the Hermite expansions
Some restriction theorems for the Heisenberg group
An analogue of Hardy's theorem for the Heisenberg group
We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on ℝⁿ related to them.
Hardy's theorem for the helgason Fourier transform on noncompact rank one symmetric spaces
Let G be a semisimple Lie group with Iwasawa decomposition G = KAN. Let X = G/K be the associated symmetric space and assume that X is of rank one. Let M be the centraliser of A in K and consider an orthonormal basis of L²(K/M) consisting of K-finite functions of type δ on K/M. For a function f on X let f̃(λ,b), λ ∈ ℂ, be the Helgason Fourier transform. Let be the heat kernel associated to the Laplace-Beltrami operator and let be the Kostant polynomials. We establish the following version...
An analogue of Gutzmer's formula for Hermite expansions
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of L²(ℝⁿ) under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.
Oscillating Multipliers for some Eigenfunction Expansions.
Analogues of Besicovitch-Wiener Theorem for Heisenberg Group.
A restriction theorem for the Heisenberg motion
We prove a restriction theorem for the class-1 representations of the Heisenberg motion group. This is done using an improvement of the restriction theorem for the special Hermite projection operators proved in [13]. We also prove a restriction theorem for the Heisenberg group.
Oscillating multipliers on the Heisenberg group
Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator is bounded on for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.
Heat kernel transform for nilmanifolds associated to the Heisenberg group.
A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on
We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on If is a Schwartz class function we show that is supported in a ball of radius in if and only if for for all This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When we show that the two conditions for imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter...
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