The idempotent multipliers on Sobolev spaces on the torus in the L¹ and uniform norms are characterized in terms of the coset ring of the dual group of the torus. This result is deduced from a more general theorem concerning certain translation invariant subspaces of vector-valued function spaces on tori.
@article{bwmeta1.element.bwnjournal-article-smv100i2p149bwm, author = {M. Wojciechowski}, title = {Translation invariant projections in Sobolev spaces on tori in the L$^1$ and uniform norms}, journal = {Studia Mathematica}, volume = {100}, year = {1991}, pages = {149-167}, zbl = {0759.46017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i2p149bwm} }
Wojciechowski, M. Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms. Studia Mathematica, Tome 100 (1991) pp. 149-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i2p149bwm/
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