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Locally convex algebras which determine a locally compact group

Gholam Hossein Esslamzadeh, Hossein Javanshiri, Rasoul Nasr-Isfahani (2016)

Studia Mathematica

There are several algebras associated with a locally compact group 𝓖 which determine 𝓖 in the category of topological groups, such as L¹(𝓖), M(𝓖), and their second duals. In this article we add a fairly large family of locally convex algebras to this list. More precisely, we show that for two infinite locally compact groups 𝓖₁ and 𝓖₂, there are infinitely many locally convex topologies τ₁ and τ₂ on the measure algebras M(𝓖₁) and M(𝓖₂), respectively, such that (M(𝓖₁),τ₁)** is isometrically...

Lp multipliers and their H1-L1 estimates on the Heisenberg group.

Chin-Cheng Lin (1995)

Revista Matemática Iberoamericana

We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.

Lp-estimates for the wave equation on the Heisenberg group.

Detlef Müller, Elias M. Stein (1999)

Revista Matemática Iberoamericana

Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that ei√£ / (1 - £)α/2 extends to a bounded operator on Lp(Hm), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.

Macdonald formula for spherical functions on affine buildings

A. M. Mantero, A. Zappa (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.

Majoration de la transformée de Fourier de certaines mesures

Noël Lohoué, Jacques Peyrière (1983)

Annales de l'institut Fourier

Soit p une fonction polynôme de R m dans R . On considère la mesure μ p sur le graphe de p dont la projection sur R m est la mesure de Lebesgue. On étudie ici le comportement de la transformée de Fourier μ ^ p ( u , v ) lorsque v approche de 0 (de telles distributions apparaissent comme caractères de représentations de groupes de Lie nilpotents). On étend des résultats de L. Corwin et F.P. Greenleaf (Comm. on Pure and Applied Math., 31 (1975), 681–705) au cas où le gradient de la partie de p homogène de plus haut degré...

Maps preserving zero products

J. Alaminos, M. Brešar, J. Extremera, A. R. Villena (2009)

Studia Mathematica

A linear map T from a Banach algebra A into another B preserves zero products if T(a)T(b) = 0 whenever a,b ∈ A are such that ab = 0. This paper is mainly concerned with the question of whether every continuous linear surjective map T: A → B that preserves zero products is a weighted homomorphism. We show that this is indeed the case for a large class of Banach algebras which includes group algebras. Our method involves continuous bilinear maps ϕ: A × A → X (for some Banach space X) with the property...

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