Moment functions of higher rank on polynomial hypergroups
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Publication:6396622
DOI10.1007/S43036-022-00204-2arXiv2204.07605WikidataQ114216155 ScholiaQ114216155MaRDI QIDQ6396622
Eszter Gselmann, Żywilla Fechner, László Székelyhidi
Publication date: 11 April 2022
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.
Harmonic analysis on hypergroups (43A62) Moment problems (44A60) Spectral synthesis on groups, semigroups, etc. (43A45)
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