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Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya"
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Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", 1985, Volume 26, Pages 57–106 (Mi intd79)  

This article is cited in 24 scientific papers (total in 24 papers)

Hypergroups and hypergroup algebras

G. L. Litvinov
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.
English version:
Journal of Soviet Mathematics, 1987, Volume 38, Issue 2, Pages 1734–1761
DOI: https://doi.org/10.1007/BF01088201
Bibliographic databases:
UDC: 517.986
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Lit85}
\by G.~L.~Litvinov
\paper Hypergroups and hypergroup algebras
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1985
\vol 26
\pages 57--106
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd79}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=849785}
\zmath{https://zbmath.org/?q=an:0628.43009}
\transl
\jour J. Soviet Math.
\yr 1987
\vol 38
\issue 2
\pages 1734--1761
\crossref{https://doi.org/10.1007/BF01088201}
Linking options:
  • https://www.mathnet.ru/eng/intd79
  • https://www.mathnet.ru/eng/intd/v26/p57
  • This publication is cited in the following 24 articles:
    1. Vit. V. Volchkov, G. V. Krasnoschyokikh, “A refinement of the two-radius theorem on the Bessel–Kingman hypergroup”, Math. Notes, 116:2 (2024), 223–237  mathnet  mathnet  crossref  crossref
    2. V. M. Buchstaber, A. P. Veselov, A. A. Gaifullin, “Classification of involutive commutative two-valued groups”, Russian Math. Surveys, 77:4 (2022), 651–727  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Rúben Sousa, Manuel Guerra, Semyon Yakubovich, Lecture Notes in Mathematics, 2315, Convolution-like Structures, Differential Operators and Diffusion Processes, 2022, 1  crossref
    4. Rúben Sousa, Manuel Guerra, Semyon Yakubovich, Lecture Notes in Mathematics, 2315, Convolution-like Structures, Differential Operators and Diffusion Processes, 2022, 9  crossref
    5. V. I. Panteleev, E. S. Taglasov, “$ES_I $-zamykanie multifunktsii ranga $2$: kriterii polnoty, klassifikatsiya i tipy bazisov”, Intellektualnye sistemy. Teoriya i prilozheniya, 25:2 (2021), 55–80  mathnet
    6. Rúben Sousa, Manuel Guerra, Semyon Yakubovich, “A unified construction of product formulas and convolutions for Sturm–Liouville operators”, Anal.Math.Phys., 11:2 (2021)  crossref
    7. V. M. Buchstaber, A. P. Veselov, “Conway topograph, $\mathrm{PGL}_2(\pmb{\mathbb Z})$-dynamics and two-valued groups”, Russian Math. Surveys, 74:3 (2019), 387–430  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. B. O. Onasanya, Y. Feng, “Some properties of fuzzy HX group”, Journal of Information and Optimization Sciences, 39:8 (2018), 1681  crossref
    9. N. Shravan Kumar, “Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II”, Can. math. bull., 60:2 (2017), 402  crossref
    10. S. MAGHSOUDI, J. B. SEOANE-SEPÚLVEDA, “HYPERGROUP ALGEBRAS AS TOPOLOGICAL ALGEBRAS”, Bull. Aust. Math. Soc., 90:3 (2014), 486  crossref
    11. M. I. Graev, G. L. Litvinov, “Integral geometry, hypergroups, and Gelfand's question”, Dokl. Math., 84:2 (2011), 660  crossref
    12. V. M. Buchstaber, “$n$-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84  mathnet  crossref  mathscinet  zmath
    13. N.J. Wildberger, “Strong hypergroups of order three”, Journal of Pure and Applied Algebra, 174:1 (2002), 95  crossref
    14. V. S. Sunder, N. J. Wildberger, Harmonic Analysis and Hypergroups, 1998, 145  crossref
    15. Nobuaki Obata, Norman J. Wildberger, “Generalized hypergroups and orthogonal polynomials”, Nagoya Mathematical Journal, 142 (1996), 67  crossref
    16. Margit Rösler, “On the dual of a commutative signed hypergroup”, Manuscripta Math, 88:1 (1995), 147  crossref
    17. Michael Voit, “A positivity result and normalization of positive convolution structures”, Math. Ann., 297:1 (1993), 677  crossref
    18. B. P. Osilenker, “A norm estimation for the generalized quasitranslation operator by orthogonal polynomials”, Funct. Anal. Appl., 26:1 (1992), 48–50  mathnet  crossref  mathscinet  zmath  isi
    19. Ajay Kumar, Lecture Notes in Mathematics, 1511, Functional Analysis and Operator Theory, 1992, 1  crossref
    20. 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  mathnet  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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