1,721,020 research outputs found
Ornstein-Uhlenbeck semigroups in infinite dimension
No full textThis is a survey paper about Ornstein-Uhlenbeck semigroups in infinite dimension and their generators. We start from the classical Ornstein-Uhlenbeck semigroup on Wiener spaces and then discuss the general case in Hilbert spaces. Finally, we present some results for Ornstein-Uhlenbeck semigroups on Banach spaces. This article is part of the theme issue 'Semigroup applications everywhere'
The Ornstein-Uhlenbeck semigroup in finite dimension
No full textWe gather the main known results concerning the non-degenerate Ornstein-Uhlenbeck semigroup in finite dimension. This article is part of the theme issue 'Semigroup applications everywhere'
Erratum: Dirichlet boundary conditions for elliptic operators with unbounded drift (Proceedings of the American Mathematical Society (2005) 133:9 (2625-2635))
No full textKernel Estimates for Schroedinger Operators
No full textWe prove short time estimates for the heat kernel of Schrödinger operators with unbounded potential in . More precisely, if we denote by the heat kernel of the Schrödinger operator , then we prove upper bounds like for a large class of potentials tending to as , under the main assumption that satisfies as and , where g is a convex function growing faster than linearly. The behaviour of c(t) near 0 is also shown to be precise. Similar bounds are also proved for the derivatives of p. Our analysis provides a family of such estimates e.g. for for every
The Ornstein-Uhlenbeck semigroup in finite dimension
No full textWe gather the main known results concerning the non-degenerate Ornstein-Uhlenbeck semigroup in finite dimension. This article is part of the theme issue 'Semigroup applications everywhere'
Global properties of invariant measures
No full textWe study global regularity properties of invariant measures associated with second order differential operators in . Under suitable conditions, we prove global boundedness of the density, Sobolev regularity, a Harnack inequality and pointwise upper and lower bounds.
Many local regularity properties are known for invariant measures, even under very weak conditions on the coefficients, see e.g. [MR1876411 (2002m:60117)]. On the other hand,
to our knowledge the only available results dealing with global regularity are [MR1351647 (96m:28015)] and [MR1391637 (98d:60120)], which have been the starting point of our investigation.
The proofs relies upon Lyapunov functions and Moser's iteration techniques
Parabolic equations in with general boundary conditions via duality methods
No full textGiven an open domain (possibly unbounded) Omega aS,R (n) , we prove that uniformly elliptic second order differential operators, under nontangential boundary conditions, generate analytic semigroups in L (1)(Omega). We use a duality method, and, further, give estimates of first order derivatives for the resolvent and the semigroup, through properties of the generator in Sobolev spaces of negative order
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