Spherical Means and the Restriction Phenomenon.
Un insieme in un gruppo si dice piccolo se esistono infiniti traslati di a due a due disgiunti. In questa nota dimostriamo in modo elementare che, sotto opportune ipotesi, non può essere l'unione di un numero finito di insiemi piccoli (e una generalizzazione di questo risultato).
We call an -multiplier m tame if for each complex homomorphism χ acting on the space of multipliers there is some and |a| ≤ 1 such that for all γ ∈ Γ. Examples of tame multipliers include tame measures and one-sided Riesz products. Tame multipliers show an interesting similarity to measures. Indeed we show that the only tame idempotent multipliers are measures. We obtain quantitative estimates on the size of -improving tame multipliers which are similar to those obtained for measures, but...
Choquet and Deny considered on an abelian locally compact topological group the representation of a measure as the convolution product of itself and a finite measure .In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions of the above equation which are relatively invariant on the support of . A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results on the above convolution...