A positivity result and normalization of positive convolution structures

1. Askey, R., Gasper, G.: Convolution structures for Laguerre polynomials. J. Anal. Math.31, 48–68 (1977)

   Google Scholar 

2. Berezansky, Yu.M., Kaluzhny, A.A.: Hypercomplex systems with locally compact bases. Sel. Math. Sov.4 (no. 2), 151–200 (1985)

   Google Scholar 

3. Berg, C., Forst, G.: Potential theory on locally compact abelian groups. Berlin Heidelberg New York: Springer 1975

   Google Scholar 

4. Bloom, W., Heyer, H.: Convolution semigroups and resolvent families of measures on hypergroups. Math. Z.188, 449–474 (1985)

   Google Scholar 

5. Dixmier, J.:C ^*-algebras. Amsterdam New York Oxford: North-Holland 1977

   Google Scholar 

6. Dunkl, C.F.: The measure algebra of a locally compact hypergroup. Trans. Am. Math. Soc.179, 331–348 (1973)

   Google Scholar 

7. Haar, H.: Über die Multiplikationstabelle der orthogonalen Funktionssysteme. Math. Z.31, 769–798 (1930)

   Google Scholar 

8. Heyer, H.: Probability measures on locally compact groups. Berlin Heidelberg New York: Springer 1977

   Google Scholar 

9. Jewett, R.I.: Spaces with an abstract convolution of measures. Adv. Math.18, 1–101 (1975)

   Google Scholar 

10. Lasser, R.: Orthogonal polynomials and hypergroups. Rend. Mat. Appl.2, 185–209 (1983)

    Google Scholar 

11. Lasser, R.: Orthogonal polynomials and hypergroups II—The symmetric case. Trans. Amer. Math. Soc. (to appear)

12. Levitan, B.M.: The application of generalized displacement operators to linear differential equations of the second order. Transl., I. Ser., Am. Math. Soc.10, 408–541 (1962)

    Google Scholar 

13. Litvinov, G.L.: Hypergroups and hypergroup algebras. J. Sov. Math.38, 1734–1761 (1987)

    Google Scholar 

14. Ross, K.A.: Hypergroups and centers of measure algebras. Symp. Math.22, 189–203 (1977)

    Google Scholar 

15. Rudin, W.: Functional analysis. New York: McGraw Hill 1973

    Google Scholar 

16. Spector, R.: Apercu de la theorie des hypergroupes. In: Eymaid, P., et al. (eds.) Analyse harmonique sur les groupes de Lie. Seminaire Nancy-Strasbourg 1973–1975. (Lect. Notes Math., vol. 497, pp. 643–673) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

17. Spector, R.: Measures invariants sur les hypergroupes. Trans. Am. Math. Soc.239, 147–166 (1978)

    Google Scholar 

18. Sunder, V.I.: II₁ factors, their bimodules, and hypergroups. Trans. Am. Math. Soc.330, 227–256 (1992)

    Google Scholar 

19. Szegö, G.: Orthogonal polynomials. (Coll. Publ., Am. Math. Soc., vol. 23) Providence, RI: Am. Math. Soc. 1959

    Google Scholar 

20. Szwarc, R.: Convolution structures and Haar matrices, J. Funct. Anal. (to appear)

21. Vilenkin, N.J.: Special functions and the theory of groups Providence, RI: Am. Math. Soc. 1968

    Google Scholar 

22. Voit, M.: Positive characters on commutative hypergroups and some applications. Math. Z.198, 405–421 (1988)

    Google Scholar 

23. Voit, M.: On the Fourier transform of positive, positive definite measures on commutative hypergroups, and dual convolution structures. Manuscr. Math.72, 141–153 (1991)

    Google Scholar 

24. Voit, M.: Pseudoisotropic random walks on free groups and semigroups. J. Multivariate Anal.38, 275–293 (1991)

    Google Scholar 

25. Voit, M.: Duals of subhypergroups and quotients of commutative hypergroups. Math. Z.210, 289–304 (1992)

    Google Scholar 

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