Dirichlet Forms Associated with Hypercontractive Semigroups
Copyright policy )Dirichlet Forms Associated with Hypercontractive Semigroups
We exhibit a class of probability measures on R n {\textbf {R}^n} such that the associated Dirichlet form is represented by a selfadjoint operator A and such that e − t A {e^{ - tA}} is a hypercontractive semigroup of operators. The measures are of the form d μ = Ω 2 d x d\mu \, = \,{\Omega ^2}\,dx where Ω \Omega has classical first derivatives and L p {L^p} second derivatives, p determined by n.
Linear symmetric and selfadjoint operators (unbounded), Groups and semigroups of linear operators, hypercontractive semigroup, General theory of partial differential operators, Dirichlet form, logarithmic Sobolev inequality, Lp-contractive semigroup
Linear symmetric and selfadjoint operators (unbounded), Groups and semigroups of linear operators, hypercontractive semigroup, General theory of partial differential operators, Dirichlet form, logarithmic Sobolev inequality, Lp-contractive semigroup
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