On the One Sided Translates of Powers of Continuous Functions on Locally Compact Groups

We prove that the one sided translates of powers of a real valued continuous (respectively compactly supported) function with a unique maximum (or minimum) span a dense subspace in C(G) and C(X) (respectively in L ^P (G) and L ^P (X)) for any locally compact group G and for any Riemannian symmetric space X.     

On furstenberg’s characterization of harmonic functions on symmetric spaces

We provide a necessary and sufficient condition on a radial probability measureμ on a symmetric space for whichf =f *μ, f bounded, implies thatf is harmonic. In particular, we obtain a short and elementary proof of a theorem of Furstenberg which says that iff is a bounded function on a symmetric space which satisfiesf =f *μ for some radialabsolutely continuous probability measureμ, thenf is harmonic.     

RNA and the Small Molecule World

A key role in essential cellular processes is played by RNA molecules, and these are attractive targets for drug design. The functional diversity of RNA can be attributed to the sophisticated three-dimensional structures it assumes. These intricate folds create potential binding pockets for ions, low molecular weight ligands, and proteins. Recent experiments have demonstrated that small molecules such as tobramycin ( 1 ) can regulate gene expression in living cells through specific interactions with a messenger RNA (mRNA).