- 期刊
RESONANCE CLASSES OF MEASURES
摘要
We extend F. Holland's definition of the space of resonant classes of functions, on the real line, to the space R(Φ_(pq)) (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(Φ_(pq)) 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.
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