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Displaying 21 – 40 of 42

A semi-group of probability measures with non-smooth differentiable densities on a Lie group

Paweł Głowacki, Andrzej Hulanicki (1987)

Colloquium Mathematicae

A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on $ℂ^{n}$

E. K. Narayanan, S. 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 $ℂ^{n} .$ If $f (z) e^{\frac{1}{4} {| z |}^{2}}$ is a Schwartz class function we show that $f$ is supported in a ball of radius $B$ in $ℂ^{n}$ if and only if $f \times μ_{r} (z) = 0$ for $r > B + | z |$ for all $z \in ℂ^{n} .$ This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When $n = 1$ we show that the two conditions $f \times μ_{r} (z) = μ_{r} \times f (z) = 0$ for $r > B + | z |$ imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter...

A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)

T. Godoy, L. Saal (2006)

Colloquium Mathematicae

Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.

A weighted multiplier theorem for Rockland operators

Krzysztof Stempak (1987)

Colloquium Mathematicae

A Wiener type theorem for (U(p,q),Hₙ)

Linda Saal (2010)

Colloquium Mathematicae

It is well known that (U(p,q),Hₙ) is a generalized Gelfand pair. Applying the associated spectral analysis, we prove a theorem of Wiener Tauberian type for the reduced Heisenberg group, which generalizes a known result for the case p = n, q = 0.

About Riesz transforms on the Heisenberg groups.

D. Müller, T. Coulhon, J. Zienkiewicz (1996)

Mathematische Annalen

Algèbres et noyaux de convolution sur le dual sphérique d’un groupe de Lie semi-simple, non compact et de rang $1$

M. Mizony (1976)

Publications du Département de mathématiques (Lyon)

Almost everywhere convergence of some summabillity methods for Laguerre series

Jolanta Długosz (1985)

Studia Mathematica

An analogue of Hardy's theorem for the Heisenberg group

S. Thangavelu (2001)

Colloquium Mathematicae

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.