Functional model for commuting isometries

Karel Horák; Vladimír Müller

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We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the $L^{2} (μ)$ space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in $L^{2} (μ)$ . A closability criterion for such forms is presented. Examples are...