DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS
Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 421-435

Voir la notice de l'article provenant de la source Cambridge University Press

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.
ALAGHMANDAN, MAHMOOD; AMINI, MASSOUD. DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS. Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 421-435. doi: 10.1017/S0017089516000252
@article{10_1017_S0017089516000252,
     author = {ALAGHMANDAN, MAHMOOD and AMINI, MASSOUD},
     title = {DUAL {SPACE} {AND} {HYPERDIMENSION} {OF} {COMPACT} {HYPERGROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {421--435},
     year = {2017},
     volume = {59},
     number = {2},
     doi = {10.1017/S0017089516000252},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000252/}
}
TY  - JOUR
AU  - ALAGHMANDAN, MAHMOOD
AU  - AMINI, MASSOUD
TI  - DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS
JO  - Glasgow mathematical journal
PY  - 2017
SP  - 421
EP  - 435
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000252/
DO  - 10.1017/S0017089516000252
ID  - 10_1017_S0017089516000252
ER  - 
%0 Journal Article
%A ALAGHMANDAN, MAHMOOD
%A AMINI, MASSOUD
%T DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS
%J Glasgow mathematical journal
%D 2017
%P 421-435
%V 59
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000252/
%R 10.1017/S0017089516000252
%F 10_1017_S0017089516000252

[1] 1. Alaghmandan, M., Approximate amenability of Segal algebras, J. Aust. Math. Soc. 95 (1) (2013), 20–35. Google Scholar

[2] 2. Alaghmandan, M., Choi, Y. and Samei, E., ZL-amenability constants of finite groups with two character degrees, Canad. Math. Bull. 57 (3) (2014), 449–462. Google Scholar

[3] 3. Alaghmandan, M. and Spronk, N., Amenability properties of the central Fourier algebra of a compact group, (to appear). Google Scholar

[4] 4. Amini, M. and Medghalchi, A. R., Amenability of compact hypergroup algebras, Math. Nachr. 287 (14–15) (2014), 1609–1617. Google Scholar | DOI

[5] 5. Azimifard, A., Samei, E. and Spronk, N., Amenability properties of the centres of group algebras, J. Funct. Anal. 256 (5) (2009), 1544–1564. Google Scholar

[6] 6. Bloom, W. R. and Heyer, H., Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics, vol. 20 (Walter de Gruyter & Co., Berlin, 1995). Google Scholar

[7] 7. Choi, Y., A gap theorem for the zl-amenability constant of a finite group, Int. J. Group Theory, 5 (4) (2016), 27–46. Google Scholar

[8] 8. Chua, K. S. and Ng, W. S., A simple proof of the uncertainty principle for compact groups, Expo. Math. 23 (2) (2005), 147–150. Google Scholar

[9] 9. Daher, R. and Kawazoe, T., An uncertainty principle on Sturm-Liouville hypergroups, Proc. Japan Acad. Ser. A Math. Sci. 83 (9–10) (2007), 167–169. Google Scholar | DOI

[10] 10. Folland, G. B., A course in abstract harmonic analysis, Studies in Advanced Mathematics (CRC Press, Boca Raton, FL, 1995). Google Scholar

[11] 11. Ghandehari, M., Hatami, H. and Spronk, N., Amenability constants for semilattice algebras, Semigroup Forum 79 (2) (2009), 279–297. Google Scholar

[12] 12. Hartmann, K., Wim Henrichs, R. and Lasser, R., Duals of orbit spaces in groups with relatively compact inner automorphism groups are hypergroups, Monatsh. Math. 88 (3) (1979), 229–238. Google Scholar

[13] 13. Hewitt, E. and Ross, K. A., Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band, vol. 152 (Springer-Verlag, New York, 1970). Google Scholar

[14] 14. Jewett, R. I., Spaces with an abstract convolution of measures, Adv. Math. 18 (1) (1975), 1–101. Google Scholar

[15] 15. Johnson, B. E., Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. (2) 50 (2) (1994), 361–374. Google Scholar

[16] 16. Kumar, A., A qualitative uncertainty principle for hypergroups, in Functional analysis and operator theory (New Delhi, 1990), Lecture Notes in Math., vol. 1511 (Springer, Berlin, 1992), 1–9. Google Scholar

[17] 17. Mosak, R. D., The L 1- and C*-algebras of [FIA]- groups, and their representations, Trans. Amer. Math. Soc. 163 (1972), 277–310. Google Scholar

[18] 18. Rösler, M. and Voit, M., An uncertainty principle for ultraspherical expansions, J. Math. Anal. Appl. 209 (2) (1997), 624–634. Google Scholar

[19] 19. Ross, K. A., Centers of hypergroups, Trans. Amer. Math. Soc. 243 (1978), 251–269. Google Scholar

[20] 20. Saeki, S., On norms of idempotent measures, Proc. Amer. Math. Soc. 19 (1968), 600–602. Google Scholar

[21] 21. Stokke, R., Approximate diagonals and Følner conditions for amenable group and semigroup algebras, Studia Math. 164 (2) (2004), 139–159. Google Scholar

[22] 22. Voit, M., An uncertainty principle for commutative hypergroups and Gel'fand pairs, Math. Nachr. 164 (1993), 187–195. Google Scholar

[23] 23. Vrem, R. C., Harmonic analysis on compact hypergroups, Pacific J. Math. 85 (1) (1979), 239–251. Google Scholar

[24] 24. Vrem, R. C., Hypergroup joins and their dual objects, Pacific J. Math. 111 (2) (1984), 483–495. Google Scholar | DOI

[25] 25. Wildberger, N. J., Finite commutative hypergroups and applications from group theory to conformal field theory, in Applications of hypergroups and related measure algebras (Seattle, WA, 1993), Contemp. Math., vol. 183 (Amer. Math. Soc., Providence, RI, 1995), 413–434. Google Scholar

Cité par Sources :