110 research outputs found
A twisted Fréchet space with basis
No full textIn this note we show that the twisted Fréchet and (LB)-spaces constructed by the second author in [6, § 1] and which were known not to have unconditional bases may, however, have a basis. © 1988 Springer-Verlag
On the extendability of conformal vector fields of 2-dimensional manifolds
No full textAbstractLet g be a pseudo-Riemannian metric on a 2-dimensional manifold M. We prove that a conformal vector field of g|M∖{p}, where p∈M, can be uniquely extended to a conformal vector field of g provided its conformal factor is bounded
Analyticity of the Cox–Ingersoll–Ross semigroup
No full textWe study the analyticity of the Cox–Ingersoll–Ross semigroup generated by Aru=ν2xu′′+γu′+βxu′-rxu,in spaces of continuous functions on [ 0 , + ∞) and we provide the full description of the domain of the generator
Kernel 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
Two-sided Gaussian bounds for fundamental solutions of non-divergence form parabolic operators with H"older continuous coefficients
No full textSome classes of non-analytic Markov semigroups
No full textAbstractWe deal with Markov semigroups Tt corresponding to second order elliptic operators Au=Δu+〈Du,F〉, where F is an unbounded locally Lipschitz vector field on RN. We obtain new conditions on F under which Tt is not analytic in Cb(RN). In particular, we prove that the one-dimensional operator Au=u″−x3u′, with domain {u∈C2(R):u, u″−x3u′∈Cb(R)}, is not sectorial in Cb(R). Under suitable hypotheses on the growth of F, we introduce a class of non-analytic Markov semigroups in Lp(RN,μ), where μ is an invariant measure for Tt
The dominant eigenvalue of nonsymmetric elliptic operators with Dirichlet boundary conditions
No full textGradient estimates for Dirichlet parabolic problems in unbounded domains
No full textAbstractWe consider autonomous parabolic Dirichlet problems in a regular unbounded open set Ω⊂RN involving second-order operator A with (possibly) unbounded coefficients. We determine new conditions on the coefficients of A yielding global gradient estimates for the bounded classical solution
Spectrum of Ornstein-Uhlenbeck Operators in Lp Spaces with Respect to Invariant Measures
No full textAbstractLet A=∑i,j=1NqijDij+∑i,j=1NbijxjDi be a possibly degenerate Ornstein–Uhlenbeck operator in RN and assume that the associated Markov semigroup has an invariant measure μ. We compute the spectrum of A in Lμp for 1⩽p<∞
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