Geodesic
Constructions of regular algebras $\mathscr L_p^w(G)$
Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 229-241

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A criterion for (Shilov) regularity of weighted algebras ${\mathscr L}_1^w(G)$ on a locally compact Abelian group $G$ is known from works of Beurling (1949) and Domar (1956). In the present paper this criterion is extended to translation-invariant weighted algebras $\mathscr L_p^w(G)$ with $p>1$. Regular algebras $\mathscr L_p^w(G)$ are constructed on any $\sigma$-compact Abelian group $G$. It was proved earlier by the author that $\sigma$-compactness is necessary (in the Abelian case) for the existence of weighted algebras $\mathscr L_p^w(G)$ with $p>1$. Bibliography: 11 titles.
Keywords: locally compact Abelian group, regular algebra, Beurling algebras, weighted algebras. 
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     author = {Yu. N. Kuznetsova},
     title = {Constructions of regular algebras $\mathscr L_p^w(G)$},
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     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_2_a3/}
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Yu. N. Kuznetsova. Constructions of regular algebras $\mathscr L_p^w(G)$. Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 229-241. http://geodesic.mathdoc.fr/item/SM_2009_200_2_a3/