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Resonance classes of measures

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  • Maria Torres De Squire

Abstract

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

Suggested Citation

  • Maria Torres De Squire, 1987. "Resonance classes of measures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-11, January.
    • Handle: RePEc:hin:jijmms:407252
    DOI: 10.1155/S0161171287000541
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