Home Convolution operators on measure algebras of KPC-hypergroups
Article
Licensed
Unlicensed Requires Authentication

Convolution operators on measure algebras of KPC-hypergroups

  • László Székelyhidi , Seyyed Mohammad Tabatabaie ORCID logo EMAIL logo and Bentol Hoda Sadathoseyni
Published/Copyright: January 10, 2018

Abstract

In this paper, we study varieties and characterize convolution operators on the algebras related to the new structures of KPC-hypergroups, which are a generalization of the classical ones.

MSC 2010: 43A62; 43A45; 44A35

References

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

[2] J. B. Conway, A Course in Point Set Topology, Undergrad. Texts Math., Springer, Cham, 2014. 10.1007/978-3-319-02368-7Search in Google Scholar

[3] C. F. Dunkl, The measure algebra of a locally compact hypergroup, Trans. Amer. Math. Soc. 179 (1973), 331–348. 10.1090/S0002-9947-1973-0320635-2Search in Google Scholar

[4] R. I. Jewett, Spaces with an abstract convolution of measures, Adv. Math. 18 (1975), no. 1, 1–101. 10.1016/0001-8708(75)90002-XSearch in Google Scholar

[5] A. A. Kalyuzhnyi, G. B. Podkolzin and Y. A. Chapovsky, Harmonic analysis on a locally compact hypergroup, Methods Funct. Anal. Topology 16 (2010), no. 4, 304–332. Search in Google Scholar

[6] A. A. Kalyuzhnyi, G. B. Podkolzin and Y. A. Chapovsky, On infinitesimal structure of a hypergroup that originates from a Lie group, Methods Funct. Anal. Topology 17 (2011), no. 4, 319–329. Search in Google Scholar

[7] R. Spector, Mesures invariantes sur les hypergroupes, Trans. Amer. Math. Soc. 239 (1978), 147–165. 10.1090/S0002-9947-1978-0463806-1Search in Google Scholar

[8] 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

[9] L. Székelyhidi, Spectral synthesis on multivariate polynomial hypergroups, Monatsh. Math. 153 (2008), no. 2, 145–152. 10.1007/s00605-007-0507-zSearch in Google Scholar

[10] L. Székelyhidi, Spectral synthesis problems on locally compact groups, Monatsh. Math. 161 (2010), no. 2, 223–232. 10.1007/s00605-009-0140-0Search in Google Scholar

[11] 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

[12] L. Székelyhidi, Spectral synthesis problems on hypergroups, Ann. Univ. Sci. Budapest. Sect. Comput. 39 (2013), 439–447. Search in Google Scholar

[13] L. Székelyhidi, Characterization of exponential polynomials on commutative hypergroups, Ann. Funct. Anal. 5 (2014), no. 2, 53–60. 10.15352/afa/1396833502Search in Google Scholar

[14] S. M. Tabatabaie and F. Haghighifar, The weighted KPC-hypergroups, Gen. Math. Notes 34 (2016), 29–38. Search in Google Scholar

[15] S. M. Tabatabaie and F. Haghighifar, The associated measure on locally compact cocommutative KPC-hypergroups, Bull. Iranian Math. Soc. 43 (2017), no. 1, 1–15. Search in Google Scholar

[16] S. M. Tabatabaie and F. Haghighifar, Translation invariant mappings on KPC-hypergroups, Int. J. Nonlinear Anal. Appl., to appear. Search in Google Scholar

[17] J. Tomiyama, On the projection of norm one in W-algebras, Proc. Japan Acad. 33 (1957), 608–612. 10.2748/tmj/1178244714Search in Google Scholar

Received: 2017-08-20
Revised: 2017-11-28
Accepted: 2017-11-29
Published Online: 2018-01-10
Published in Print: 2019-01-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 4.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/apam-2017-0087/html?lang=en
Scroll to top button