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| 概要 |
Let $ X= {X_k(ω,t)}_{t in T} $, $ k in N $, be an independent sequence of Gaussian processes with mean 0 on a locally compact separable metric space $ (T,d) $, and assume that the covariance functions... are non-negative and $ sum _k[X_k( omega ,s) X_k( omega ,t)] = u \times log^{+} {1/d(s,t)}+O(1) $, $ s,t in T $ for a positeve number $ u<0 $. Kahane [1985] defined a multiplicative chaos by $ X $ and gave sufficient conditions for the regularity or the singularity of a measure with respect to it in the case where $ (T, d) $ is compact and homogeneous in the sense of Coifman and Weiss. The aim of this paper are to interprete Kahane's results from the viewpoint of the dimension of a measure, and extend them to the case where $ (T, d) $ is a locally compact metric space equipped with a majorizing measure and not necessarily homogeneous.続きを見る
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