Resonance classes of measures - Maria Torres De Squire (International Journal of Mathematics and Mathematical Sciences)
We extend F. Holland's definition of the space of resonant classes of functions, on the real line, to the space R(Φpq) (1≦p, q≦∞) of resonant classes of measures, on locally compact abelian groups. We characterize this space in terms of transformable measures and establish a realatlonship between R(Φpq) and the set of positive definite functions for amalgam spaces. As a consequence we answer the conjecture posed by L. Argabright and J. Gil de Lamadrid in their work on Fourier analysis of unbounded measures.