Ditkin’s condition for certain Beurling algebras
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- by Sen-Zhong Huang, Jan van Neerven and Frank Räbiger PDF
- Proc. Amer. Math. Soc. 126 (1998), 1397-1407 Request permission
Abstract:
Let $G$ be a locally compact abelian group. A function $\omega :G\to [1,\infty )$ is said to be a weight if it is locally bounded, Borel measurable and submultiplicative. We call a weight $\omega$ on $G$ semi-bounded if there exist a constant $K$ and a subsemigroup $S$ with $S-S=G,$ such that \[ \omega (s)\leq K\quad \text {and}\quad \lim _{n\to \infty }\frac {\log \omega (-ns)}{\sqrt {n}}=0\] for all $s\in S.$ Using functional analytic methods, we show that all Beurling algebras $\lg$ whose defining weight $\omega$ is semi-bounded satisfy Ditkin’s condition.References
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Additional Information
- Sen-Zhong Huang
- Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, F. R. Germany
- Address at time of publication: Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 1-4, D-07743 Jena, Germany
- Email: huang@mipool.uni-jena.de
- Jan van Neerven
- Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, F. R. Germany
- Address at time of publication: Department of Mathematics, Tu Delft, P. O. Box 356, 2600 AJ Delft, the Netherlands
- Email: J.vanNeerven@twi.tudelft.nl
- Frank Räbiger
- Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, F. R. Germany
- Email: frra@michelangelo.mathematik.uni-tuebingen.de
- Received by editor(s): October 14, 1996
- Additional Notes: This research is supported by Deutscher Akademischer Austauschdienst DAAD (first author) and by the Human Capital Mobility Programme of the European Community (second author). It is part of a research project supported by Deutsche Forschungsgemeinschaft DFG (third author).
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1397-1407
- MSC (1991): Primary 43A45, 43A20, 47D03
- DOI: https://doi.org/10.1090/S0002-9939-98-04237-3
- MathSciNet review: 1443833