Continuity of convolution semigroups on hypergroups |
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| Authors: | Walter R Bloom Herbert Heyer |
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| Institution: | (1) School of Mathematical and Physical Sciences, Murdoch University, 6150 Perth, Western Australia, Australia;(2) Mathematisches Institut, Universität Tübingen, D-7400 Tübingen 1, Germany |
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| Abstract: | LetK be a commutative hypergroup with the property that either the identity character is contained in the support of the Plancherel measure onK
^, or the identity character is not isolated inK
^ and all characters sufficiently close (but not equal) to the identity character vanish at infinity. We present a shift compactness theorem forK and use this to prove that every symmetric convolution semigroup of probability measures onK is continuous. |
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| Keywords: | Harmonic analysis probability measure hypergroup convolution semigroup tight shift compact |
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