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Moment functions on hypergroup joins

  • Kedumetse Vati EMAIL logo and László Székelyhidi


Moment functions play a basic role in probability theory. A natural generalization can be defined on hypergroups which leads to the concept of generalized moment function sequences. In a former paper we studied some function classes on hypergroup joins which play a basic role in spectral synthesis. Moment functions are also important basic blocks of spectral synthesis. All these functions can be characterized by well-known functional equations. In this paper we describe generalized moment function sequences on hypergroup joins.

MSC 2010: 20N20; 39B99


[1] J. Aczél, Functions of binomial type mapping groupoids into rings, Math. Z. 154 (1977), no. 2, 115–124. 10.1007/BF01241825Search in Google Scholar

[2] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, De Gruyter Stud. Math. 20, Walter de Gruyter, Berlin, 1995. 10.1515/9783110877595Search in Google Scholar

[3] Z. Fechner and L. Székelyhidi, Sine functions on hypergroups, Arch. Math. (Basel) 106 (2016), no. 4, 371–382. 10.1007/s00013-016-0884-4Search in Google Scholar

[4] L. Gallardo, Asymptotic drift of the convolution and moment functions on hypergroups, Math. Z. 224 (1997), no. 3, 427–444. 10.1007/PL00004292Search in Google Scholar

[5] L. Gallardo, Some methods to find moment functions on hypergroups, Harmonic Analysis and Hypergroups (Delhi 1995), Trends Math., Birkhäuser, Boston (1998), 13–31. 10.1007/978-0-8176-4348-5_2Search in Google Scholar

[6] H. Heyer and S. Kawakami, Extensions of Pontryagin hypergroups, Probab. Math. Statist. 26 (2006), no. 2, 245–260. Search in Google Scholar

[7] A. Orosz and L. Székelyhidi, Moment functions on polynomial hypergroups in several variables, Publ. Math. Debrecen 65 (2004), no. 3–4, 429–438. 10.5486/PMD.2004.3170Search in Google Scholar

[8] A. Orosz and L. Székelyhidi, Moment functions on polynomial hypergroups, Arch. Math. (Basel) 85 (2005), no. 2, 141–150. 10.1007/s00013-005-1441-8Search in Google Scholar

[9] A. Orosz and L. Székelyhidi, Moment functions on Sturm–Liouville hypergroups, Ann. Univ. Sci. Budapest. Sect. Comput. 29 (2008), 141–156. Search in Google Scholar

[10] L. Székelyhidi, Functional equations on hypergroups, Functional Equations, Inequalities and Applications, Kluwer, Dordrecht (2003), 167–181. 10.1007/978-94-017-0225-6_12Search in Google Scholar

[11] L. Székelyhidi, Spectral analysis and spectral synthesis on polynomial hypergroups, Monatsh. Math. 141 (2004), no. 1, 33–43. 10.1007/s00605-002-0003-4Search in Google Scholar

[12] L. Székelyhidi, Functional Equations on Hypergroups, World Scientific, New Jersey, 2012. Search in Google Scholar

[13] L. Székelyhidi, Exponential polynomials on commutative hypergroups, Arch. Math. (Basel) 101 (2013), no. 4, 341–347. 10.1007/s00013-013-0559-3Search in Google Scholar

[14] L. Székelyhidi, Harmonic and Spectral Analysis, World Scientific, New Jersey, 2014. 10.1142/8924Search in Google Scholar

[15] L. Székelyhidi and K. Vati, Functional equations on hypergroup joins, Arch. Math. (Basel) 109 (2017), no. 1, 41–47. 10.1007/s00013-017-1022-7Search in Google Scholar

[16] M. Voit, Substitution of open subhypergroups, Hokkaido Math. J. 23 (1994), no. 1, 143–183. 10.14492/hokmj/1381412491Search in Google Scholar

[17] M. Voit, Sine functions on compact commutative hypergroups, Arch. Math. (Basel) 107 (2016), no. 3, 259–263. 10.1007/s00013-016-0918-ySearch in Google Scholar

[18] R. C. Vrem, Hypergroup joins and their dual objects, Pacific J. Math. 111 (1984), no. 2, 483–495. 10.2140/pjm.1984.111.483Search in Google Scholar

[19] H. Zeuner, Moment functions and laws of large numbers on hypergroups, Math. Z. 211 (1992), no. 3, 369–407. 10.1007/BF02571436Search in Google Scholar

Received: 2018-02-07
Revised: 2018-04-08
Accepted: 2018-04-12
Published Online: 2018-05-03
Published in Print: 2019-07-01

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