EuDML | Browse

Let $G$ be a locally compact group. Let $L_{t}$ be the left translation in $L^{\infty} (G)$ , given by $L_{t} f (x) = f (t x)$ . We characterize (undre a mild set-theoretical hypothesis) the functions $f \in L^{\infty} (G)$ such that the map $t \to L_{t} f$ from $G$ into $L^{\infty} (G)$ is scalarly measurable (i.e. for $φ \in L^{\infty} (G)^{*}$ , $t \to φ (L_{t} f)$ is measurable). We show that it is the case when $t \to θ (L_{f} t)$ is measurable for each character $θ$ , and if $G$ is compact, if and only if $f$ is Riemann-measurable. We show that $t \to L_{t} f$ is Borel measurable if and only if $f$ is left uniformly continuous.Some of the measure-theoretic tools used there...

Complemented Subspaces of L... (G), Ideals of L... (G) and Amenability.

Mohammed E.B. Bekka (1990)

Monatshefte für Mathematik

Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one.

Michael Cowling, Uffe Haagerup (1989)

Inventiones mathematicae

Construction of Sobolev spaces of fractional order with sub-riemannian vector fields

Sami Mustapha, François Vigneron (2007)

Annales de l’institut Fourier

Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.

Displaying 1 – 14 of 14

Central Fourier Analysis for Lorentz Spaces on Compact Lie Groups.

Central Lacunary Sets.

Characterization of amenable groups and the Littlewood functions on free groups

Characterization of measures in the group C*-algebra of a locally compact group.

Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations

Complemented Subspaces of L... (G), Ideals of L... (G) and Amenability.

Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one.

Construction of Sobolev spaces of fractional order with sub-riemannian vector fields

Continuity of Operators Commuting with Translations for Compact Groups.

Continuity of Translation Invariant Linear Functionals on C... (G) for Certain Locally Compact Groups G.

Convolution of functions in Lorentz spaces

Convolution Semigroups of Local Type.

Convolutions and factorization theorems

Correction to the paper "The structure space of the trigonometric polynomials on a comapct group".

Currently displaying 1 – 14 of 14