Analyticity of non-symmetric Ornstein-Uhlenbeck semigroup with respect\n to a weighted Gaussian measure

2019/02/06 by Davide Addona, Addona, Davide
Mathematics · #Spectral Theory in Mathematical Physics #advanced mathematical theories #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.1902.02364

Abstract

In this paper we show that the realization in L^p(X,\ν_\∞) of the\nnonsymmetric Ornstein-Uhlenbeck operator L is sectorial for any\np\∈(1,+\∞) and we provide an explicit sector of analyticity. Here\n(X,\μ_\∞,H_\∞) is an abstract Wiener space, i.e., X is a separable\nBanach space, \μ_\∞ is a centred non degenerate Gaussian measure on X\nand H_\∞ is the associated Cameron-Martin space. Further, \ν_\∞ is\na weighted Gaussian measure, that is, \ν_\∞=e^-U\μ_\∞ where U\nis a convex function which satisfies some minimal conditions. Our results\nstrongly rely on the theory of nonsymmetric Dirichlet forms and on the\ndivergence form of the realization of L in L²(X,\ν_\∞).\n

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