Support properties of the free measure for Boson fields |
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Authors: | M. Reed L. Rosen |
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Affiliation: | 1. Mathematics Department, Princeton University, Princeton, N.J. 2. Mathematics Department, University of Toronto, Toronto, Canada
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Abstract: | Let μ be the measure onI′ (? d ) corresponding to the Gaussian process with mean zero and covariance (f,(?Δ+1)?1 g) onI (? d ). It is proven that the set $$( - Delta _{d - 1} + 1)^{d/4 - tfrac{1}{2} + alpha } (1 + x^2 )^{d/4} [log (2 + x^2 )]^beta L^2 (mathbb{R}^d )$$ has μ measure one if α>0 and β>1/2 and μ measure zero if α>0 and β<1/2; here Δ d?1 is the Laplacian in anyd?1 dimensions whend>1 and Δ0=Δ. |
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