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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 $\int L_{x} h \cdot g \leq C_{h} \int h g$ 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...

Displaying 1 – 6 of 6

On a translation property of positive definite functions

On Integrable Representations.

On Isolated Points in the Dual Spaces of Locally Compact Groups.

On LCA groups each of whose characters is ultimately measurable

On Mackey topologies in topological abelian groups.

On Separation in Reduced Duals of Groups with Compact Invariant Neighbourhoods of the Identity.

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