Additions and corrections to: “On the ideal structure of the algebra of radial functions”

Schwartz, Alan L.

doi:10.1090/S0002-9939-1973-0313718-X

Additions and corrections to: “On the ideal structure of the algebra of radial functions”
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by Alan L. Schwartz PDF

Proc. Amer. Math. Soc. 39 (1973), 288-294 Request permission

Abstract:

The corrections and additions are made in the context of Hankel transforms which generalize the Fourier transforms of radial functions. The following question is studied: given two closed ideals ${I_1}$ and ${I_2}$ in the algebra of Hankel transforms such that both have the same spectrum and ${I_1} \subset {I_2}$, when is there a closed ideal $I$ such that ${I_1} \subset I \subset {I_2}$?

References

Roger Godement, Théorèmes taubériens et théorie spectrale, Ann. Sci. École Norm. Sup. (3) 64 (1947), 119–138 (1948) (French). MR 0023242, DOI 10.24033/asens.945
Henry Helson, On the ideal structure of group algebras, Ark. Mat. 2 (1952), 83–86. MR 49912, DOI 10.1007/BF02591383
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Sadahiro Saeki, An elementary proof of a theorem of Henry Helson, Tohoku Math. J. (2) 20 (1968), 244–247. MR 231139, DOI 10.2748/tmj/1178243181

Local properties of Hankel transform

Alan L. Schwartz, The smoothness of Hankel transforms, J. Math. Anal. Appl. 28 (1969), 500–507. MR 249963, DOI 10.1016/0022-247X(69)90004-3
Alan Schwartz, On the ideal structure of the algebra of radial functions, Proc. Amer. Math. Soc. 26 (1970), 621–624. MR 265865, DOI 10.1090/S0002-9939-1970-0265865-6
Alan Schwartz, The structure of the algebra of Hankel transforms and the algebra of Hankel-Stieltjes transforms, Canadian J. Math. 23 (1971), 236–246. MR 273312, DOI 10.4153/CJM-1971-023-x
N. Th. Varopoulos, Spectral synthesis on spheres, Proc. Cambridge Philos. Soc. 62 (1966), 379–387. MR 201908, DOI 10.1017/s0305004100039967