Opuscula Math. 43, no. 4 (2023), 493-505
https://doi.org/10.7494/OpMath.2023.43.4.493
Opuscula Mathematica
Generalized derivations and generalized exponential monomials on hypergroups
Żywilla Fechner
Eszter Gselmann
László Székelyhidi
Abstract. 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.
Keywords: moment function, moment sequence, exponential monomial, exponential polynomial, derivation, higher order derivation, hypergroup.
Mathematics Subject Classification: 39B52, 39B72, 43A45, 43A70.
- W.R. Bloom, H. Heyer, Harmonic analysis of probability measures on hypergroups, volume 20 of De Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin, 1995.
- Ż. Fechner, E. Gselmann, L. Székelyhidi, Endomorphisms of the measure algebra of commutative hypergroups (2022), arXiv:2204.07499.
- L. Székelyhidi, Functional Equations on Hypergroups, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
- L. Székelyhidi, Harmonic and Spectral Analysis, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2014.
- K. Vati, L. Székelyhidi, Exponential monomials on hypergroup joins, Miskolc Math. Notes 21 (2020), no. 1, 463-472. https://doi.org/10.18514/MMN.2020.3011
- Żywilla Fechner
https://orcid.org/0000-0001-7412-6544- Lodz University of Technology, Institute of Mathematics, al. Politechniki 10, 93-590 Łódź, Poland
- Eszter Gselmann (corresponding author)
- https://orcid.org/0000-0002-1708-2570
- Institute of Mathematics, University of Debrecen, H-4002 Debrecen, P.O. Box: 400, Hungary
- László Székelyhidi
- https://orcid.org/0000-0001-8078-6426
- Institute of Mathematics, University of Debrecen, H-4002 Debrecen, P.O. Box: 400, Hungary
- Communicated by Marek Galewski.
- Received: 2022-10-20.
- Accepted: 2023-04-21.
- Published online: 2023-06-13.
