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| SMOOTH POINT MEASURES AND DIFFEOMORPHISM GROUPS |
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Citation： |
Zhang Yingnan.SMOOTH POINT MEASURES AND DIFFEOMORPHISM GROUPS[J].Chinese Annals of Mathematics B,1984,5(1):7~16 |
| Page view： 700
Net amount： 808 |
Authors： |
Zhang Yingnan; |
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| Abstract： |
Let $\[X = {R^d}(d > 1)\]$. Consider the unitary representations of Diff(X) given by quasi-invariant measures under the action of Diff(X). The author proposes smooth point measures as generalization of Poisson point measures and proves that every smooth point measure is
quasi-invariant under the action of Diff(X) and if $\[\{ U_g^i\} \]$ ,i=1,2, are the unitar representations of Diff(X) given by the smooth point measures $\[{\mu _i}\]$, i=l,2, respectively, then $\[\{ U_g^1\} \]$ is unitarily equivalent to $\[\{ U_g^2\} \]$ iff $\[{\mu _1}\]$ is equivalent to $\[{\mu _2}\]$ as measure. |
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