CHARACTERIZING COMPACT FAMILIESVIA THE LAPLACE TRANSFORM

摘要

In 1985, Pego characterized compact families in L2(R) in terms of the Fourier transform. It took nearly 30 years to realize that Pego's result can be proved in a more general setting of locally compact abelian groups (works of Grka and Kostrzewa). In the current paper, we argue that the Fourier transform is not the only integral transform that is efficient in characterizing compact families and suggest the Laplace transform as a possible alternative.