Abstract
In this paper we consider generalized moment functions of higher order. These functions are closely related to the well-known functions of binomial type which have been investigated on various abstract structures. In our former paper we investigated the properties of generalized moment functions of higher order on commutative groups. In particular, we proved the characterization of generalized moment functions on a commutative group as the product of an exponential and composition of multivariate Bell polynomial and a sequence additive functions. In the present paper we continue the study of generalized moment function sequences of higher order in the more abstract setting, namely we consider functions defined on a hypergroup. We characterize these functions on the polynomial hypergroup in one variable by means of partial derivatives of a composition of polynomials generating the polynomial hypergroup and an analytic function. As an example, we give an explicit formula for moment generating functions of rank at most two on the Tchebyshev hypergroup.
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Acknowledgements
The research of E. Gselmann has partially been carried out with the help of the project 2019-2.1.11-TÉT-2019-00049, which has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the TÉT funding scheme. The research of E. Gselmann and L. Székelyhidi has been supported by the NKFIH (Nemzeti Kutatási, Fejlesztési és Innovációs Hivatal) Grant no. K 134191.
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The authors received the following grant support: The research of E. Gselmann has partially been carried out with the help of the project 2019-2.1.11-TÉT-2019-00049, which has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the TÉT funding scheme. The research of E. Gselmann and L. Székelyhidi has been supported by the NKFIH (Nemzeti Kutatási, Fejlesztési és Innovációs Hivatal) Grant no. K 134191. All authors prepared the manuscript under the obligations arising from the employment in the below mentioned affiliated research institutes.
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Communicated by M. S. Moslehian.
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Fechner, Ż., Gselmann, E. & Székelyhidi, L. Moment functions of higher rank on polynomial hypergroups. Adv. Oper. Theory 7, 41 (2022). https://doi.org/10.1007/s43036-022-00204-2
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DOI: https://doi.org/10.1007/s43036-022-00204-2