Resonance classes of measures

Maria Torres De Squire

International Journal of Mathematics and Mathematical Sciences, 1987, vol. 10, 1-11

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.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:407252

DOI: 10.1155/S0161171287000541

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