Geodesic
Some questions of spectral synthesis on spheres
Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 317-338 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper considers the Banach algebra $L^1(R^n)$ with the usual norm and convolution as multiplication. A characterization is given for closed ideals of $L^1(R^n)$ which are rotation invariant and have $S^{n-1}$ as spectrum, in terms of annihilators of certain collections of pseudomeasures. The main result of the paper is connected with a construction which yields an uncountable chain of closed ideals intermediate between neighboring invariant closed ideals with spectrum $S^{n-1}$. This construction associates an ideal $I(E)$ with a closed subset $E\subset S^{n-1}$. It is shown that if $\operatorname{int}E_1\neq\operatorname{int}E_2$ then $I(E_1)\neq I(E_2)$. Another result is the lack of a continuous projection from the largest to the smallest ideal when $n =3$, and when $n>3$, from an invariant ideal onto the neighboring smaller invariant ideal. A certain algebra of functions on the sphere which arises naturally in the construction of the intermediate ideals is also studied. Bibliography: 18 titles. 
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     author = {V. F. Osipov},
     title = {Some questions of spectral synthesis on spheres},
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     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_2_a9/}
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V. F. Osipov. Some questions of spectral synthesis on spheres. Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 317-338. http://geodesic.mathdoc.fr/item/SM_1973_21_2_a9/

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