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On a semigroup of measures with irregular densities

Przemysław Gadziński (2000)

Colloquium Mathematicae

We study the densities of the semigroup generated by the operator - X 2 + | Y | on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are C . We give explicit spectral decomposition of images of - X 2 + | Y | in representations.

On Schwartz's theorem for the motion group

Yitzhak Weit (1980)

Annales de l'institut Fourier

Schwartz’s Theorem in spectral synthesis of continuous functions on the real is generalized to the Euclidean motion group. The rightsided analogue of Schwartz’s Theorem for the motion group is reduced to the study of some invariant subspaces of continuous functions on R 2 .

Opérateurs invariants sur certains immeubles affines de rang 2

Ferdaous Kellil, Guy Rousseau (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

On considère un immeuble Δ de type A 2 ˜ ou B 2 ˜ , différents sous-ensembles 𝒮 de l’ensemble 𝒮 des sommets de Δ et différents groupes G d’automorphismes de Δ , très fortement transitifs sur Δ . On montre que l’algèbre des opérateurs G -invariants agissant sur l’espace des fonctions sur 𝒮 est souvent non commutative (contrairement aux résultats classiques). Dans certains cas on décrit sa structure et on détermine ses fonctions radiales propres. On en déduit que la conjecture d’Helgason n’est pas toujours vérifiée...

Oscillating multipliers on the Heisenberg group

E. K. Narayanan, S. 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.

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