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On a translation property of positive definite functions

Lars Omlor, Michael Leinert (2010)

Banach Center Publications

If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant C h > 0 such that L x h · g C h h g for every continuous positive definite g≥0, where L x is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That “for one h” implies “for all h” seemed obvious, but turned out not to be obvious at all. We fill...

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