Resonance classes of measures
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 betwe...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000541 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |