Abstract:
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous representations of topological hypergroup algebras.
Citation:
G. L. Litvinov, “Hypergroups and hypergroup algebras”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 26, VINITI, Moscow, 1985, 57–106; J. Soviet Math., 38:2 (1987), 1734–1761
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V. M. Buchstaber, A. P. Veselov, A. A. Gaifullin, “Classification of involutive commutative two-valued groups”, Russian Math. Surveys, 77:4 (2022), 651–727
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V. I. Panteleev, E. S. Taglasov, “ESI-zamykanie multifunktsii ranga 2: kriterii polnoty, klassifikatsiya i tipy bazisov”, Intellektualnye sistemy. Teoriya i prilozheniya, 25:2 (2021), 55–80
Rúben Sousa, Manuel Guerra, Semyon Yakubovich, “A unified construction of product formulas and convolutions for Sturm–Liouville operators”, Anal.Math.Phys., 11:2 (2021)
V. M. Buchstaber, A. P. Veselov, “Conway topograph, PGL2(ZZ)-dynamics and two-valued groups”, Russian Math. Surveys, 74:3 (2019), 387–430
B. O. Onasanya, Y. Feng, “Some properties of fuzzy HX group”, Journal of Information and Optimization Sciences, 39:8 (2018), 1681
N. Shravan Kumar, “Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II”, Can. math. bull., 60:2 (2017), 402
S. MAGHSOUDI, J. B. SEOANE-SEPÚLVEDA, “HYPERGROUP ALGEBRAS AS TOPOLOGICAL ALGEBRAS”, Bull. Aust. Math. Soc., 90:3 (2014), 486
M. I. Graev, G. L. Litvinov, “Integral geometry, hypergroups, and Gelfand's question”, Dokl. Math., 84:2 (2011), 660
V. M. Buchstaber, “n-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84
N.J. Wildberger, “Strong hypergroups of order three”, Journal of Pure and Applied Algebra, 174:1 (2002), 95
V. S. Sunder, N. J. Wildberger, Harmonic Analysis and Hypergroups, 1998, 145
Nobuaki Obata, Norman J. Wildberger, “Generalized hypergroups and orthogonal polynomials”, Nagoya Mathematical Journal, 142 (1996), 67
Margit Rösler, “On the dual of a commutative signed hypergroup”, Manuscripta Math, 88:1 (1995), 147
Michael Voit, “A positivity result and normalization of positive convolution structures”, Math. Ann., 297:1 (1993), 677
B. P. Osilenker, “A norm estimation for the generalized quasitranslation operator by orthogonal polynomials”, Funct. Anal. Appl., 26:1 (1992), 48–50
Ajay Kumar, Lecture Notes in Mathematics, 1511, Functional Analysis and Operator Theory, 1992, 1
G. B. Podkolzin, “An infinitesimal object of the hypercomplex system, generated by double cosets, and nonlinear differential equations”, Funct. Anal. Appl., 25:1 (1991), 78–80
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