Fourier-Stieltjes localization in neighborhoods of finite-dimensional irreducible representations of locally compact groups

An analog of the localization principle for the almost convergence for any element of the Fourier-Stieltjes algebra (Fourier-Stieltjes transforms of bounded measures) is established for any unimodular amenable locally compact groups in neighborhoods of finite-dimensional representations of these groups. To the blessed memory of Yuri Solov’ev Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting the Leading Scientific Schools under grant no. NSh 619.203.1, and by the INTAS grant.