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The Sector of Analyticity of the Ornstein–Uhlenbeck Semigroup on L p Spaces with Respect to Invariant Measure
Author(s) -
Chill R.,
Fašangová E.,
Metafune G.,
Pallara D.
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006344
Subject(s) - semigroup , mathematics , ornstein–uhlenbeck process , invariant measure , measure (data warehouse) , invariant (physics) , gaussian , generator (circuit theory) , mathematical analysis , pure mathematics , mathematical physics , stochastic process , physics , statistics , quantum mechanics , database , computer science , ergodic theory , power (physics)
The sector of analyticity of the Ornstein–Uhlenbeck semigroup is computed on the spaceL μ p := L p (R N ; μ) with respect to its invariant measure μ. If A=Δ + Bx· ∇ denotes the generator of the Ornstein–Uhlenbeck semigroup, then the angle Θ 2 of the sector of analyticity inL μ 2is π/2 minus the spectral angle of BQ ∞ , Q ∞ being the matrix determining the Gaussian measure μ. The angle of analyticity inL μ pis then given by the formulacot θ p =( p − 2 ) 2 + p 2( cot θ 2 ) 22 p − 1