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Zbl 1230.43005
Yang, Dilian
(Yang, Di-lian)
Cosine functions revisited. (English)
[J] Banach J. Math. Anal. 5, No. 2, 126-130, electronic only (2011). ISSN 1735-8787/e

The author gives an elementary proof of the small dimension lemma: If $K$ is a closed, irreducible subgroup of $SU(n)$, where $n\in\bbfN$, such that $k+ k^{-1}\in\bbfC I$ for all $k\in K$, then $n=1$, or $n=2$ and $K\subseteq SU(2)$.\par She uses the lemma in a short proof of one of her earlier results about the structure of non-zero continuous cosine functions on a compact group $G$: Each such one is the normalized character of a continuous representation of $G$ into $SU(2)$.
[Henrik Stetkaer (Aarhus)]

MSC 2000:: *43A30 Fourier type transforms on nonabelian groups, etc.
39B52 Functional equations for functions with more general domains
22C05 Compact topological groups
47D09 Operator cosine functions and higher-order Cauchy problems

Keywords: cosine function; non-abelian Fourier transform; representation of a compact group

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Zentralblatt MATH Berlin [Germany]