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Spherical functions and the Fourier algebra

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In questo lavoro viene data una dimostrazione della regolarità locale della trasformata di Fourier di una funzione radiale inR n mediante l'uso della formula di inversione per la trasformata di Radon. Si dimostra che tali tecniche consentono di estendere questo risultato al caso delle trasformate di Fourier di funzioniAd(G)-invarianti definite sull'algebra di Lie di un gruppo di Lie compatto connesso semisemplice. E' data infine una descrizione in termini di trasformate sferiche inverse degli elementi bi-K-invarianti dell'algebra di Fourier diG quando (G,K) è una coppia di Gel'fand.

Summary

We show how the inversion formula for the Radon transform of radial functions can be used to demonstrate local regularity for radial Fourier transforms and a similar result forAd(G)-invariant Fourier transforms on the Lie algebra of a compact semisimple connected Lie groupG. We also sketch the description of the bi-K-invariant elements of the Fourier algebra ofG as inverse spherical transforms, when (G,K) are a Gel'fand pair.

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Authors and Affiliations

  1. dell'Università di Adelaide, (Australia)

    Christopher Meaney

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  1. Christopher Meaney
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(Conferenza tenuta l'11 giugno 1984)

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Meaney, C. Spherical functions and the Fourier algebra. Seminario Mat. e. Fis. di Milano 54, 127–132 (1985). https://doi.org/10.1007/BF02924853

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