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A decomposition theorem for compact groups with an application to supercompactness

Wiesław Kubiś, Sławomir Turek (2011)

Open Mathematics

We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.

An extension of deLeeuw’s theorem to the n -dimensional rotation group

Anthony H. Dooley, Garth I. Gaudry (1984)

Annales de l'institut Fourier

We study a method of approximating representations of the group M ( n ) by those of the group S O ( n + 1 ) . As a consequence we establish a version of a theorem of DeLeeuw for Fourier multipliers of L p that applies to the “restrictions” of a function on the dual of M ( n ) to the dual of S O ( n + 1 ) .

An F. and M. Riesz theorem for bounded symmetric domains

R. G. M. Brummelhuis (1987)

Annales de l'institut Fourier

We generalize the classical F. and M. Riesz theorem to metrizable compact groups whose center contains a copy of the circle group. Important examples of such groups are the isotropy groups of the bounded symmetric domains.The proof uses a criterion for absolute continuity involving L p spaces with p < 1 : A measure μ on a compact metrisable group K is absolutely continuous with respect to Haar measure d k on K if for some p < 1 a certain subspace of L p ( K , d k ) which is related to μ has sufficiently many continuous linear...

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