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• # Artykuł - szczegóły

## Colloquium Mathematicum

2012 | 129 | 1 | 119-131

## Strongly invariant means on commutative hypergroups

EN

### Abstrakty

EN
We introduce and study strongly invariant means m on commutative hypergroups, $m(T_{x}φ · ψ) = m(φ · T_{x̃}ψ)$, x ∈ K, $φ,ψ ∈ L^{∞}(K)$. We show that the existence of such means is equivalent to a strong Reiter condition. For polynomial hypergroups we derive a growth condition for the Haar weights which is equivalent to the existence of strongly invariant means. We apply this characterization to show that there are commutative hypergroups which do not possess strongly invariant means.

119-131

wydano
2012

### Twórcy

autor
• Helmholtz National Research Center, for Environment and Health, Institute of Biomathematics and Biometry, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany
• Munich University of Technology, Centre of Mathematics, 85748 Garching, Germany
autor
• Helmholtz National Research Center for Environment and Health, Institute of Biomathematics and Biometry, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany