International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 461-471

Resonance classes of measures

Maria Torres De Squire

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.


We extend F. Holland's definition of the space of resonant classes of functions, on the real line, to the space R(Φpq) (1p, 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.