International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 461-471
doi:10.1155/S0161171287000541
Resonance classes of measures
Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Saskatchewan, Canada
Received 30 September 1986
Copyright © 1987 Maria Torres De Squire. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.