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Exponentially bounded positive-definite functions on a commutative hypergroup

  • Walter R. Bloom (a1) and Paul Ressel (a2)

Abstract

In this paper we make use of semigroup methods on the space of compactly supported measures to obtain a Bochner representation for α-bounded positive-definite functions on a commutative hypergroup.

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Copyright

References

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[1]Bloom, W. R. and Heyer, H., ‘Characterisation of potential kernels of transient convolution semigroups on a commutative hypergroup’, Probability measures on groups, IX (Proc. Conf., Oberwolfach, 1988), Lecture Notes in Math. 1379 (Springer, Berlin, 1989), pp. 2135.
[2]Bloom, W. R. and Ressel, P., ‘Positive definite and related functions on hypergroups’, Canad. J. Math. 43 (1991), 242254.
[3]Hewitt, E. and Ross, K. A., Abstract harmonic analysis, vol 1. Structure of topological groups. Integration theory, group representations, Die Gundlehren der mathematischen Wissenschaften 115 (Springer, Berlin, 1963).
[4]Hoffmann-Jørgensen, J., The theory of analytic spaces, Var. Publ. Series 10 (Matematisk Institut, Århus Universitet, 1970).
[5]Jewett, R. I., ‘Spaces with an abstract convolution of measures’, Adv. Math. 18 (1975), 1101.
[6]Reiter, H., Classical harmonic analysis and locally compact groups, Oxford Mathematical Monographs (Clarendon Press, Oxford, 1968).
[7]Ressel, P., ‘Integral representations on convex semigroups’, Math. Scand. 61 (1987), 93111.
[8]Ross, K. A., ‘Centers of hypergroups’, Trans. Amer. Math. Soc. 243 (1978), 251269.
[9]Spector, R., ‘Mesures invariantes sur les hypergroupes’, Trans. Amer. Math. Soc. 239 (1978), 147165.
[10]Voit, M., ‘Positive characters on commutative hypergroups and some applications’, Math. Z. 198 (1988), 405421.
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Exponentially bounded positive-definite functions on a commutative hypergroup

  • Walter R. Bloom (a1) and Paul Ressel (a2)

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