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Positive Definite and Related Functions on Hypergroups

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

Abstract

In this paper we make use of semigroup methods on the space of compactly supported probability measures to obtain a complete Lévy-Khinchin representation for negative definite functions on a commutative hypergroup. In addition we obtain representation theorems for completely monotone and completely alternating functions. The techniques employed here also lead to considerable simplification of the proofs of known results on positive definite and negative definite functions on hypergroups.

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References

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1. Berg, Christian, Reus Christensen, Jens Peter and Ressel, Paul, Harmonic analysis on semigroups. Graduate Texts in Mathematics, 100, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984.
2. Bloom, Walter R. and Herbert Heyer, Characterisation of potential kernels of transient convolution semigroups on a commutative hypergroup. Probability measures on groups IX (Proc. Conf., Oberwolfach Math. Res. Inst., Oberwolfach 1988), Lecture Notes in Math., 1379, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989, 21-35.
3. Buchwalter, Henri, Les fonctions de Levy existent!, Math. Ann. 274(1986), 3134.
4. Hewitt, Edwin and Ross, Kenneth A., Abstract harmonic analysis, vol II. Die Grundlehren der mathematischen Wissenschaften, 152, Springer-Verlag, Berlin, Heidelberg, New York, 1970.
5. Heyer, Herbert, Probability measures on locally compact groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, 94, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
6. Jewett, Robert I., Spaces with an abstract convolution of measures, Adv. in Math. 18(1975), 1101.
7. Lasser, Rupert, Orthogonal polynomials and hypergroups, Rend. Mat. (Series VII)3(1983), 185209.
8. Lasser, Rupert, Convolution semigroups on hypergroups, Pacific J. Math. 127(1987), 353371.
9. Ressel, Paul, Integral representations on convex semigroups, Math. Scand. 61(1987), 93111.
10. Spector, René, Mesures invariantes sur les hypergroupes, Trans. Amer. Math. Soc. 239(1978), 147165.
11. Voit, Michael, Positive characters on commutative hypergroups and some applications, Math. Z. 198( 1988), 405421.
12. Voit, Michael, Negative definite functions on commutative hypergroups. Probability measures on groups IX(Proc. Conf., Oberwolfach Math. Res. Inst., Oberwolfach 1988), Lecture Notes in Math., 1379, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989, 376388.
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