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Generalized derivations and generalized exponential monomials on hypergroups

Fechner Żywilla, Gselmann Eszter, Székelyhidi László

Opuscula Mathematica

2023

Vol. 43, no. 4

493--505

In one of our former papers Endomorphisms of the measure algebra of commutative hypergroups we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra. Continuing with this, we are now looking for the connection between the generalized exponential polynomials of a commutative hypergroup and the higher order derivations of the corresponding measure algebra.

Probability on matrix-cone hypergroups: limit theorems and structural properties

Hazod W.

Journal of Applied Analysis

2009

Vol. 15, nr 2

205-245

Recent investigations of M. Rösler [13] and M. Voit [17] provide examples of hypergroups with properties similar to the group-or vector space case and with a sufficiently rich structure of automorphisms, providing thus tools to investigate the limit theory of normalized random walks and the structure of the corresponding limit, laws. The investigations are parallel to corresponding investigations for vector spaces and simply connected nilpotent Lie groups.