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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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000541 |
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| _version_ | 1849412802962259968 |
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| author | Maria Torres De Squire |
| author_facet | Maria Torres De Squire |
| author_sort | Maria Torres De Squire |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-549a35de844f4e019fc1853e70a7b912 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-549a35de844f4e019fc1853e70a7b9122025-08-20T03:34:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110346147110.1155/S0161171287000541Resonance classes of measuresMaria Torres De Squire0Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Saskatchewan, CanadaWe 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.http://dx.doi.org/10.1155/S0161171287000541amalgam spacesFourier transform of unbounded measurespositive definite measurespositive definite quasimeasuresFourier multipliers. |
| spellingShingle | Maria Torres De Squire Resonance classes of measures International Journal of Mathematics and Mathematical Sciences amalgam spaces Fourier transform of unbounded measures positive definite measures positive definite quasimeasures Fourier multipliers. |
| title | Resonance classes of measures |
| title_full | Resonance classes of measures |
| title_fullStr | Resonance classes of measures |
| title_full_unstemmed | Resonance classes of measures |
| title_short | Resonance classes of measures |
| title_sort | resonance classes of measures |
| topic | amalgam spaces Fourier transform of unbounded measures positive definite measures positive definite quasimeasures Fourier multipliers. |
| url | http://dx.doi.org/10.1155/S0161171287000541 |
| work_keys_str_mv | AT mariatorresdesquire resonanceclassesofmeasures |