The heat operator in infinite dimensions

Details The heat operator in infinite dimensions The heat operator in infinite dimensions

2007-10-10

arxiv.org/abs/0710.2137v1

Infinite Dimensional Analysis in Honor of H.-H. Kuo, edited by A. N. Sengupta and P. Sundar, World Scientific 2008, pp. 161-17

Physics

Mathematical Physics

Scientific paper

Let (H,B) be an abstract Wiener space and let \mu_{s} be the Gaussian measure on B with variance s. Let \Delta be the Laplacian (*not* the number operator), that is, a sum of squares of derivatives associated to an orthonormal basis of H. I will show that the heat operator \exp(t\Delta/2) is a contraction operator from L^2(B,\mu_{s} to L^2(B,\mu_{s-t}), for all t

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