THE SECTOR OF ANALYTICITY OF THE ORNSTEIN–UHLENBECK SEMIGROUP ON Lp SPACES WITH RESPECT TO INVARIANT MEASURE

The sector of analyticity of the Ornstein–Uhlenbeck semigroup is computed on the space Lp μ :=Lp(RN ; μ) with respect to its invariant measure μ. If A=Δ+Bx·∇ denotes the generator of the Ornstein–Uhlenbeck semigroup, then the angle θ2 of the sector of analyticity in L2 μ is π/2 minus the spectral angle of BQ∞, Q∞ being the matrix determining the Gaussian measure μ. The angle of analyticity in Lp μ is then given by the formula cot θp = (p − 2)2 + p2(cot θ2)2 2 √ p − 1 .